A008776 -id:A008776 - cp's OEIS frontend

A001023 Powers of 14.

1, 14, 196, 2744, 38416, 537824, 7529536, 105413504, 1475789056, 20661046784, 289254654976, 4049565169664, 56693912375296, 793714773254144, 11112006825558016, 155568095557812224, 2177953337809371136, 30491346729331195904, 426878854210636742656, 5976303958948914397184, 83668255425284801560576

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 14), L(1, 14), P(1, 14), T(1, 14). Essentially same as Pisot sequences E(14, 196), L(14, 196), P(14, 196), T(14, 196). See A008776 for definitions of Pisot sequences.
Number of n-permutations of 15 objects: l, m, n, o, p, q, r, s, t, u, v, w, z, x, y with repetition allowed and containing no u's, (u-free). Permutations with repetitions! If n=0 then 1 >>14^0=1 "". (no u's.) If n=1 then 13 >>14^1=14, >> l, m, n, o, p, q, r, s, t, v, w, z, x, y. (no u's.) etc. - Zerinvary Lajos, Jul 01 2009
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 14-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..100
Peter J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 278.
Tanya Khovanova, Recursive Sequences.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Yash Puri and Thomas Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for linear recurrences with constant coefficients, signature (14).

Cf. A000005, A000290, A160193.

Row 9 of A329332.

[ 14^n: n in [0..20] ]; // Vincenzo Librandi, Nov 21 2010

[ n eq 1 select 1 else 14*Self(n-1): n in [1..21] ];

A001023:=-1/(-1+14*z); # conjectured by Simon Plouffe in his 1992 dissertation

Table[14^n,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
Denominator/@HermiteH[Range[0,20],5/28] (* Harvey P. Dale, Jul 11 2011 *)

a(n)=14^n \\ Charles R Greathouse IV, Nov 18 2011

print([14**n for n in range(21)]) # Michael S. Branicky, Jan 14 2021

[lucas_number1(n,14,0) for n in range(1, 18)]# Zerinvary Lajos, Apr 29 2009

G.f.: 1/(1-14x), e.g.f.: exp(14x)
A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller, Mar 04 2007
a(n) = 14^n; a(n) = 14*a(n-1) with a(0)=1. - Vincenzo Librandi, Nov 21 2010

More terms from James Sellers, Sep 19 2000

A001026 Powers of 17.

Original entry on oeis.org

1, 17, 289, 4913, 83521, 1419857, 24137569, 410338673, 6975757441, 118587876497, 2015993900449, 34271896307633, 582622237229761, 9904578032905937, 168377826559400929, 2862423051509815793, 48661191875666868481, 827240261886336764177, 14063084452067724991009, 239072435685151324847153, 4064231406647572522401601

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 17), L(1, 17), P(1, 17), T(1, 17). Essentially same as Pisot sequences E(17, 289), L(17, 289), P(17, 289), T(17, 289). See A008776 for definitions of Pisot sequences.
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 17-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
Numbers n such that sigma(17*n) = 17*n + sigma(n). - Jahangeer Kholdi, Nov 23 2013

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..100
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 281
Tanya Khovanova, Recursive Sequences
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for linear recurrences with constant coefficients, signature (17).

[17^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

A001026:=-1/(-1+17*z); [Simon Plouffe in his 1992 dissertation.]

Table[17^n,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)

A001026(n):=17^n$
makelist(A001026(n),n,0,30); /* Martin Ettl, Nov 05 2012 */

a(n)=17^n \\ Charles R Greathouse IV, Sep 24 2015

[lucas_number1(n,17,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

G.f.: 1/(1-17x), e.g.f.: exp(17x).
a(n)=17^n ; a(n)=17*a(n-1) n>0, a(0)=1. - Vincenzo Librandi, Nov 21 2010
G.f.: 1 + x*(G(0) - 1)/(x-1) where G(k) = 1 - (4(k+1)^2+1)/(1-x/(x - 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jan 15 2013

More terms from James Sellers, Sep 19 2000

A009965 Powers of 21.

Original entry on oeis.org

1, 21, 441, 9261, 194481, 4084101, 85766121, 1801088541, 37822859361, 794280046581, 16679880978201, 350277500542221, 7355827511386641, 154472377739119461, 3243919932521508681, 68122318582951682301, 1430568690241985328321, 30041942495081691894741, 630880792396715529789561, 13248496640331026125580781, 278218429446951548637196401

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 21), L(1, 21), P(1, 21), T(1, 21). Essentially same as Pisot sequences E(21, 441), L(21, 441), P(21, 441), T(21, 441). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 21-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

T. D. Noe, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (21).

Row 10 of A329332.

[21^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010

21^Range[0,20] (* or *) NestList[21#&,1,20] (* Harvey P. Dale, Aug 31 2023 *)

A009965(n):=21^n$
makelist(A009965(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

a(n)=21^n \\ Charles R Greathouse IV, Nov 18 2011

[lucas_number1(n,21,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

For A009966..A009992 we have g.f.: 1/(1-qx), e.g.f.: exp(qx), with q = 21, 22, ..., 48. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 07 2001
a(n) = 21^n; a(n) = 21*a(n-1), n > 0, a(0)=1. - Vincenzo Librandi, Nov 21 2010
G.f.: 22/G(0) where G(k) = 1 - 2*x*(k+1)/(1 - 1/(1 - 2*x*(k+1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 10 2013

A009969 Powers of 25.

Original entry on oeis.org

1, 25, 625, 15625, 390625, 9765625, 244140625, 6103515625, 152587890625, 3814697265625, 95367431640625, 2384185791015625, 59604644775390625, 1490116119384765625, 37252902984619140625, 931322574615478515625, 23283064365386962890625, 582076609134674072265625, 14551915228366851806640625, 363797880709171295166015625, 9094947017729282379150390625

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 25), L(1, 25), P(1, 25), T(1, 25). Essentially same as Pisot sequences E(25, 625), L(25, 625), P(25, 625), T(25, 625). See A008776 for definitions of Pisot sequences.
A000005(a(n)) = A005408(n+1). - Reinhard Zumkeller, Mar 04 2007
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 25-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

T. D. Noe, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (25).

Bisection of A000351 (powers of 5).

Cf. A218728 (partial sums).

[25^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010

25^Range[0,20] (* or *) NestList[25#&,1,20] (* Harvey P. Dale, Dec 12 2016 *)

a(n)=25^n \\ Charles R Greathouse IV, Sep 24 2015

[lucas_number1(n,25,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

G.f.: 1/(1-25*x). - Philippe Deléham, Nov 23 2008
E.g.f.: exp(25*x). - Zerinvary Lajos, Apr 29 2009
a(n) = 25^n; a(n) = 25*a(n-1), n > 0; a(0)=1. - Vincenzo Librandi, Nov 21 2010
a(n) = A000351(2n) = 5^(2n). - M. F. Hasler, Sep 02 2021

A009971 Powers of 27.

Original entry on oeis.org

1, 27, 729, 19683, 531441, 14348907, 387420489, 10460353203, 282429536481, 7625597484987, 205891132094649, 5559060566555523, 150094635296999121, 4052555153018976267, 109418989131512359209, 2954312706550833698643, 79766443076872509863361, 2153693963075557766310747

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 27), L(1, 27), P(1, 27), T(1, 27). Essentially same as Pisot sequences E(27, 729), L(27, 729), P(27, 729), T(27, 729). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 27-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

T. D. Noe, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (27).

Cf. A000244, A001019, A008585, A008776.

[27^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

27^Range[0, 20] (* Paolo Xausa, Jul 19 2024 *)

a(n)=27^n \\ Charles R Greathouse IV, Sep 24 2015

[lucas_number1(n,27,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

G.f.: 1/(1-27*x). - Philippe Deléham, Nov 24 2008
a(n) = 27^n; a(n) = 27*a(n-1), n > 0; a(0)=1. - Vincenzo Librandi, Nov 21 2010
From Elmo R. Oliveira, Jul 10 2025: (Start)
E.g.f.: exp(27*x).
a(n) = A000244(n)*A001019(n) = A000244(A008585(n)). (End)

A009968 Powers of 24: a(n) = 24^n.

Original entry on oeis.org

1, 24, 576, 13824, 331776, 7962624, 191102976, 4586471424, 110075314176, 2641807540224, 63403380965376, 1521681143169024, 36520347436056576, 876488338465357824, 21035720123168587776, 504857282956046106624, 12116574790945106558976, 290797794982682557415424, 6979147079584381377970176, 167499529910025153071284224, 4019988717840603673710821376

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 24), L(1, 24), P(1, 24), T(1, 24). Essentially same as Pisot sequences E(24, 576), L(24, 576), P(24, 576), T(24, 576). See A008776 for definitions of Pisot sequences.
If X_1, X_2, ..., X_n is a partition of the set {1, 2, ..., 2*n} into blocks of size 2 then, for n >= 1, a(n) is equal to the number of functions f : {1, 2, ..., 2*n} -> {1, 2, 3, 4, 5} such that for fixed y_1, y_2, ..., y_n in {1, 2, 3, 4, 5} we have f(X_i) <> {y_i}, (i = 1, 2, ..., n). - Milan Janjic, May 24 2007
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 24-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

T. D. Noe, Table of n, a(n) for n = 0..100
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (24).

Column k = 4 of A225816.

[24^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

NestList[24#&, 1, 20] (* Harvey P. Dale, Feb 04 2017 *)

a(n)=24^n \\ Charles R Greathouse IV, Sep 24 2015

[24**n for n in range(21)] # Michael S. Branicky, Jan 24 2021

[lucas_number1(n,24,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

LazyList.iterate(1: BigInt)( * 24).take(24).toList // _Alonso del Arte, Apr 24 2020

G.f.: 1/(1 - 24*x). - Philippe Deléham, Nov 23 2008
E.g.f.: exp(24x). - Zerinvary Lajos, Apr 29 2009
a(n) = 24^n; a(n) = 24*a(n-1) for n > 0, a(0) = 1. - Vincenzo Librandi, Nov 21 2010
a(n) = det(|s(i + 4, j)|, 1 <= i, j <= n), where s(n, k) are Stirling numbers of the first kind. - Mircea Merca, Apr 04 2013

A016089 Numbers n such that n divides n-th Lucas number A000032(n).

Original entry on oeis.org

1, 6, 18, 54, 162, 486, 1458, 1926, 4374, 5778, 13122, 17334, 39366, 52002, 118098, 156006, 206082, 354294, 468018, 618246, 1062882, 1404054, 1854738, 2471058, 3188646, 4212162, 5564214, 7413174, 9565938, 12636486, 16692642, 22050774

Offset: 1

Robert G. Wilson v

nonn

Note that if n divides A000032(n) and p is an odd prime divisor of A000032(n), then pn divides A000032(pn) and, furthermore, p^k*n divides A000032(p^k*n) for every integer k>=0.
In particular, since 6 divides A000032(6) = 2*3^2, A016089 includes all terms of the geometric progression 2*3^k for k>0 (see A099856); since 18 divides A000032(18) = 2*3^3*107, A016089 includes all terms of the form 2*107^m*3^k for k>1 and m>=0; etc.
Terms of A016089 starting with 18 are multiples of 18. There are no other terms of the form 18p where p is prime, except for p=3 and p=107. - Alexander Adamchuk, May 11 2007

Lars Blomberg, Table of n, a(n) for n = 1..91
Dov Jarden, Recurring Sequences, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See p. 75.
C. Smyth, The terms in Lucas Sequences divisible by their indices, JIS 13 (2010) #10.2.4.

Cf. A000032, A000204, A025192, A008776.

Cf. A099856, A072378 = numbers n such that 12n divides Fibonacci(12n), A023172 = numbers n such that n divides Fibonacci(n).

a = 1; b = 3; Do[c = a + b; a = b; b = c; If[Mod[c, n] == 0, Print[n]], {n, 3, 2, 10^6}]

is(n)=(Mod([0,1;1,1],n)^n*[2;1])[1,1]==0 \\ Charles R Greathouse IV, Nov 04 2016

Extended and revised by Max Alekseyev, May 13 2007, May 15 2008, May 16 2008

A001027 Powers of 18.

Original entry on oeis.org

1, 18, 324, 5832, 104976, 1889568, 34012224, 612220032, 11019960576, 198359290368, 3570467226624, 64268410079232, 1156831381426176, 20822964865671168, 374813367582081024, 6746640616477458432, 121439531096594251776, 2185911559738696531968, 39346408075296537575424, 708235345355337676357632, 12748236216396078174437376

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 18), L(1, 18), P(1, 18), T(1, 18). Essentially same as Pisot sequences E(18, 324), L(18, 324), P(18, 324), T(18, 324). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 18-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..100
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 282
Tanya Khovanova, Recursive Sequences
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for linear recurrences with constant coefficients, signature (18).

[ 18^n: n in [0..20] ]; // Vincenzo Librandi, Nov 21 2010

A001027:=-1/(-1+18*z); # Simon Plouffe in his 1992 dissertation

Table[18^n,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)

a(n)=18^n \\ Charles R Greathouse IV, Sep 28 2015

[18**n for n in range(20)] # F. Chapoton, Feb 23 2020

[lucas_number1(n,18,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

G.f.: 1/(1-18x), e.g.f.: exp(18x).

a(n) = 18^n; a(n) = 18*a(n-1) with a(0)=1. - Vincenzo Librandi, Nov 21 2010

More terms from James Sellers, Sep 19 2000

A004119 a(0) = 1; thereafter a(n) = 3*2^(n-1) + 1.

Original entry on oeis.org

1, 4, 7, 13, 25, 49, 97, 193, 385, 769, 1537, 3073, 6145, 12289, 24577, 49153, 98305, 196609, 393217, 786433, 1572865, 3145729, 6291457, 12582913, 25165825, 50331649, 100663297, 201326593, 402653185, 805306369, 1610612737, 3221225473, 6442450945, 12884901889

Offset: 0

N. J. A. Sloane, R. K. Guy

Also Pisot sequence L(4,7) (cf. A008776).
Alternatively, define the sequence S(a(1),a(2)) by: a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n > 0. This is S(4,7).
a(n) = number of terms of the arithmetic progression with first term 2^(2n-1) and last term 2^(2n+1). So common difference is 2^n. E.g., a(2)=7 corresponds to (8,12,16,20,24,28,32). - Augustine O. Munagi, Feb 21 2007
Equals binomial transform of [1, 3, 0, 3, 0, 3, 0, 3, ...]. - Gary W. Adamson, Aug 27 2010

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993
S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663.
S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663. [Annotated scanned copy]
A. O. Munagi and T. Shonhiwa, On the partitions of a number into arithmetic progressions, J. Integer Sequences, 11 (2008), #08.5.4.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (3, -2).
Index entries for Pisot sequences

Cf. A049988, A049775, A000051, A008776.
A181565 is an essentially identical sequence.
For primes see A002253 and A039687.

[1] cat [n le 1 select 4 else 2*Self(n-1)-1: n in [1..40]]; // Vincenzo Librandi, Dec 16 2015

A004119:=-(-1-z+3*z**2)/(2*z-1)/(z-1); # Simon Plouffe in his 1992 dissertation

s=4;lst={1,s};Do[s=s+(s-1);AppendTo[lst,s],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 30 2009 *)
Prepend[Table[3*2^n + 1, {n, 0, 32}], 1] (* or *)
{1}~Join~LinearRecurrence[{3, -2}, {4, 7}, 33] (* Michael De Vlieger, Dec 16 2015 *)

a(n)=3<Charles R Greathouse IV, Sep 28 2015

a(n) = 3a(n-1) - 2a(n-2).
For n>3, a(3)=13, a(n)= a(n-1)+2*floor(a(n-1)/2). - Benoit Cloitre, Aug 14 2002
For n>=1, a(n) = A049775(n+1)/2^(n-2). For n>=2, a(n) = 2a(n-1)-1; see also A000051. - Philippe Deléham, Feb 20 2004
O.g.f.: -(-1-x+3*x^2)/((2*x-1)*(x-1)). - R. J. Mathar, Nov 23 2007
For n>0, a(n) = 2*a(n-1)-1. - Vincenzo Librandi, Dec 16 2015
E.g.f.: exp(x)*(1 + 3*sinh(x)). - Stefano Spezia, May 06 2023

Edited by N. J. A. Sloane, Dec 16 2015 at the suggestion of Bruno Berselli

A009976 Powers of 32.

Original entry on oeis.org

1, 32, 1024, 32768, 1048576, 33554432, 1073741824, 34359738368, 1099511627776, 35184372088832, 1125899906842624, 36028797018963968, 1152921504606846976, 36893488147419103232, 1180591620717411303424, 37778931862957161709568, 1208925819614629174706176, 38685626227668133590597632

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 32), L(1, 32), P(1, 32), T(1, 32). Essentially same as Pisot sequences E(32, 1024), L(32, 1024), P(32, 1024), T(32, 1024). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 32-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

			a(6) = 32^6 = 1073741824.

T. D. Noe, Table of n, a(n) for n = 0..100
Philip DeOrsey, Stephen G. Hartke, and Jason Williford, A Classification of Hyperfocused 12-Arcs, arXiv:2105.08300 [math.CO], 2021.
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (32).

Subsequence of A000079.

Cf. A001025, A008587, A008776, A089357.

[32^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

A009976:=n->32^n; seq(A009976(k), k=0..50); # Wesley Ivan Hurt, Nov 04 2013

Table[32^n, {n,0,50}] (* Wesley Ivan Hurt, Nov 04 2013 *)

A009976(n):=32^n$
makelist(A009976(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

a(n)=32^n \\ Charles R Greathouse IV, Sep 24 2015

def A009976(n): return 1<<5*n # Chai Wah Wu, Nov 10 2022

[lucas_number1(n,32,0) for n in range(1, 17)] # Zerinvary Lajos, Nov 07 2009

G.f.: 1/(1-32*x). - Philippe Deléham, Nov 24 2008
a(n) = 32^n; a(n) = 32*a(n-1) for n > 0, a(0)=1. - Vincenzo Librandi, Nov 21 2010
From Elmo R. Oliveira, Jul 08 2025: (Start)
E.g.f.: exp(32*x).
a(n) = 2^A008587(n) = A000079(n)*A001025(n) = A089357(n)/A000079(n). (End)

cp's OEIS Frontend

A001023 Powers of 14.

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A001026 Powers of 17.

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A009965 Powers of 21.

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A009969 Powers of 25.

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A009971 Powers of 27.

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A009968 Powers of 24: a(n) = 24^n.

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