A013730 -id:A013730 - cp's OEIS frontend

A016921 a(n) = 6*n + 1.

1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 187, 193, 199, 205, 211, 217, 223, 229, 235, 241, 247, 253, 259, 265, 271, 277, 283, 289, 295, 301, 307, 313, 319, 325, 331

Offset: 0

N. J. A. Sloane

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 22 ).
Also solutions to 2^x + 3^x == 5 (mod 7). - Cino Hilliard, May 10 2003
Except for 1, exponents n > 1 such that x^n - x^2 - 1 is reducible. - N. J. A. Sloane, Jul 19 2005
Let M(n) be the n X n matrix m(i,j) = min(i,j); then the trace of M(n)^(-2) is a(n-1) = 6*n - 5. - Benoit Cloitre, Feb 09 2006
If Y is a 3-subset of an (2n+1)-set X then, for n >= 3, a(n-1) is the number of 3-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007
All composite terms belong to A269345 as shown in there. - Waldemar Puszkarz, Apr 13 2016
First differences of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 773", based on the 5-celled von Neumann neighborhood. - Robert Price, May 23 2016
For b(n) = A103221(n) one has b(a(n)-1) = b(a(n)+1) = b(a(n)+2) = b(a(n)+3) = b(a(n)+4) = n+1 but b(a(n)) = n. So-called "dips" in A103221. See the Avner and Gross remark on p. 178. - Wolfdieter Lang, Sep 16 2016
A (n+1,n) pebbling move involves removing n + 1 pebbles from a vertex in a simple graph and placing n pebbles on an adjacent vertex. A two-player impartial (n+1,n) pebbling game involves two players alternating (n+1,n) pebbling moves. The first player unable to make a move loses. The sequence a(n) is also the minimum number of pebbles such that any assignment of those pebbles on a complete graph with 3 vertices is a next-player winning game in the two player impartial (k+1,k) pebbling game. These games are represented by A347637(3,n). - Joe Miller, Oct 18 2021
Interleaving of A017533 and A017605. - Leo Tavares, Nov 16 2021

			From _Ilya Gutkovskiy_, Apr 15 2016: (Start)
Illustration of initial terms:
                      o
                    o o o
              o     o o o
            o o o   o o o
      o     o o o   o o o
    o o o   o o o   o o o
o   o o o   o o o   o o o
n=0  n=1     n=2     n=3
(End)

Avner Ash and Robert Gross, Summing it up, Princeton University Press, 2016, p. 178.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Kayla Barker, Mia DeStefano, Eugene Fiorini, Michael Gohn, Joe Miller, Jacob Roeder, and Tony W. H. Wong, Generalized Impartial Two-player Pebbling Games on K_3 and C_4, J. Int. Seq. (2024) Vol. 27, Issue 5, Art. No. 24.5.8. See p. 3.
Tanya Khovanova, Recursive Sequences.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database.
Leo Tavares, Illustration: Hexagonal Lines.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A093563 ((6, 1) Pascal, column m=1).
Cf. A000567 (partial sums), A002476 (primes), A005408, A008588, A016813, A016933, A016945, A016957, A017281, A017533, A128470, A158057, A161700, A161705, A161709, A161714.
a(n) = A007310(2*(n+1)); complement of A016969 with respect to A007310.
Cf. A287326 (second column).
Cf. A000217, A003215.
Cf. A001477, A017605.

List([0..60], n-> 6*n+1); # G. C. Greubel, Sep 18 2019

a016921 = (+ 1) . (* 6)
a016921_list = [1, 7 ..]  -- Reinhard Zumkeller, Jan 15 2013

[6*n+1: n in [0..60]]; // G. C. Greubel, Sep 18 2019

a[1]:=1:for n from 2 to 100 do a[n]:=a[n-1]+6 od: seq(a[n], n=1..56); # Zerinvary Lajos, Mar 16 2008

Range[1, 500, 6] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)

a(n)=6*n+1 \\ Charles R Greathouse IV, Mar 22 2016

for n in range(0,10**5):print(6*n+1) # Soumil Mandal, Apr 14 2016

a(n) = 6*n + 1, n >= 0 (see the name).
G.f.: (1+5*x)/(1-x)^2.
A008615(a(n)) = n. - Reinhard Zumkeller, Feb 27 2008
A157176(a(n)) = A013730(n). - Reinhard Zumkeller, Feb 24 2009
a(n) = 4*(3*n-1) - a(n-1) (with a(0)=1). - Vincenzo Librandi, Nov 20 2010
E.g.f.: (1 + 6*x)*exp(x). - G. C. Greubel, Sep 18 2019
a(n) = A003215(n) - 6*A000217(n-1). See Hexagonal Lines illustration. - Leo Tavares, Sep 10 2021
From Leo Tavares, Oct 27 2021: (Start)
a(n) = 6*A001477(n-1) + 7
a(n) = A016813(n) + 2*A001477(n)
a(n) = A017605(n-1) + A008588(n-1)
a(n) = A016933(n) - 1
a(n) = A008588(n) + 1. (End)
Sum_{n>=0} (-1)^n/a(n) = Pi/6 + sqrt(3)*arccoth(sqrt(3))/3. - Amiram Eldar, Dec 10 2021

A001018 Powers of 8: a(n) = 8^n.

Original entry on oeis.org

1, 8, 64, 512, 4096, 32768, 262144, 2097152, 16777216, 134217728, 1073741824, 8589934592, 68719476736, 549755813888, 4398046511104, 35184372088832, 281474976710656, 2251799813685248, 18014398509481984, 144115188075855872, 1152921504606846976, 9223372036854775808, 73786976294838206464, 590295810358705651712, 4722366482869645213696

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 8), L(1, 8), P(1, 8), T(1, 8). Essentially same as Pisot sequences E(8, 64), L(8, 64), P(8, 64), T(8, 64). See A008776 for definitions of Pisot sequences.
If X_1, X_2, ..., X_n is a partition of the set {1..2n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1..2n} -> {1,2,3} such that for fixed y_1,y_2,...,y_n in {1,2,3} we have f(X_i)<>{y_i}, (i=1..n). - Milan Janjic, May 24 2007
This is the auto-convolution (convolution square) of A059304. - R. J. Mathar, May 25 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 8-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
a(n) is equal to the determinant of a 3 X 3 matrix with rows 2^(n+2), 2^(n+1), 2^n; 2^(n+3), 2^(n+4), 2(n+3); 2^n, 2^(n+1), 2^(n+2) when it is divided by 144. - J. M. Bergot, May 07 2014
a(n) gives the number of small squares in the n-th iteration of the Sierpinski carpet fractal. Equivalently, the number of vertices in the n-Sierpinski carpet graph. - Allan Bickle, Nov 27 2022

			For n=1, the 1st order Sierpinski carpet graph is an 8-cycle.

K. H. Rosen et al., eds., Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2017; p. 15.
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
Allan Bickle, Degrees of Menger and Sierpinski Graphs, Congr. Num. 227 (2016) 197-208.
Allan Bickle, MegaMenger Graphs, The College Mathematics Journal, 49 1 (2018) 20-26.
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 273
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Tanya Khovanova, Recursive Sequences
Caroline Nunn, A Proof of a Generalization of Niven's Theorem Using Algebraic Number Theory, Rose-Hulman Undergraduate Mathematics Journal: Vol. 22, Iss. 2, Article 3 (2021). See table at p. 9.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Eric Weisstein's World of Mathematics, Sierpiński Carpet
Index entries for linear recurrences with constant coefficients, signature (8).

Cf. A013730, A103333, A013731, A067417, A083233, A055274.
Cf. A008588, A016969, A157176.
Cf. A000079 (powers of 2), A000244 (powers of 3), A000302 (powers of 4), A000351 (powers of 5), A000400 (powers of 6), A000420 (powers of 7), A001019 (powers of 9), ..., A001029 (powers of 19), A009964 (powers of 20), ..., A009992 (powers of 48), A087752 (powers of 49), A165800 (powers of 50), A159991 (powers of 60).
Cf. A032766 (floor(3*n/2)).
Cf. A271939 (number of edges in the n-Sierpinski carpet graph).

a001018 = (8 ^)
a001018_list = iterate (* 8) 1  -- Reinhard Zumkeller, Apr 29 2015

[8^n : n in [0..30]]; // Wesley Ivan Hurt, Sep 27 2016

seq(8^n, n=0..23); # Nathaniel Johnston, Jun 26 2011
A001018 := n -> 8^n; # M. F. Hasler, Apr 19 2015

Table[8^n, {n,0,50}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)

makelist(8^n,n,0,20); /* Martin Ettl, Nov 12 2012 */

a(n)=8^n \\ Charles R Greathouse IV, May 10 2014

print([8**n for n in range(25)]) # Michael S. Branicky, Dec 29 2021

a(n) = 8^n.
a(0) = 1; a(n) = 8*a(n-1) for n > 0.
G.f.: 1/(1-8*x).
E.g.f.: exp(8*x).
Sum_{n>=0} 1/a(n) = 8/7. - Gary W. Adamson, Aug 29 2008
a(n) = A157176(A008588(n)); a(n+1) = A157176(A016969(n)). - Reinhard Zumkeller, Feb 24 2009
From Stefano Spezia, Dec 28 2021: (Start)
a(n) = (-1)^n*(1 + sqrt(-3))^(3*n) (see Nunn, p. 9).
a(n) = (-1)^n*Sum_{k=0..floor(3*n/2)} (-3)^k*binomial(3*n, 2*k) (see Nunn, p. 9). (End)

A016933 a(n) = 6*n + 2.

Original entry on oeis.org

2, 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 86, 92, 98, 104, 110, 116, 122, 128, 134, 140, 146, 152, 158, 164, 170, 176, 182, 188, 194, 200, 206, 212, 218, 224, 230, 236, 242, 248, 254, 260, 266, 272, 278, 284, 290, 296, 302, 308, 314, 320, 326

Offset: 0

N. J. A. Sloane

Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (11;0). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1Sergey Kitaev, Nov 11 2004
Exponents n>1 for which 1 - x + x^n is reducible. - Ron Knott, Oct 13 2016
For the Collatz problem, these are the descenders' values that require division by 2. - Fred Daniel Kline, Jan 19 2017
For n > 3, also the number of (not necessarily maximal) cliques in the n-helm graph. - Eric W. Weisstein, Nov 29 2017

Michael De Vlieger, Table of n, a(n) for n = 0..10000
Gennady Eremin, Infinite matrix of odd natural numbers. A bit about Sophie Germain prime numbers, arXiv:2501.17090 [math.GM], 2025. See p. 9.
Tanya Khovanova, Recursive Sequences.
Sergey Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 4 (2004), Article A21, 20pp.
Sergey Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014.
Eric Weisstein's World of Mathematics, Clique.
Eric Weisstein's World of Mathematics, Helm Graph.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008588, A016921, A016945, A016957, A016969, A017569, A016777, A016813.

a016933 = (+ 2) . (* 6)  -- Reinhard Zumkeller, Jul 05 2013

a[1]:=2:for n from 2 to 100 do a[n]:=a[n-1]+6 od: seq(a[n], n=1..47); # Zerinvary Lajos, Mar 16 2008

Range[2, 500, 6] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
Table[6 n + 2, {n, 0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
6 Range[0, 20] + 2 (* Eric W. Weisstein, Nov 29 2017 *)
LinearRecurrence[{2, -1}, {8, 14}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[2 (1 + 2 x)/(-1 + x)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)

a(n)=6*n+2 \\ Charles R Greathouse IV, Jul 10 2016

[i+2 for i in range(280) if gcd(i,6) == 6] # Zerinvary Lajos, May 20 2009

A008615(a(n)) = n+1. - Reinhard Zumkeller, Feb 27 2008
A157176(a(n)) = A013730(n). - Reinhard Zumkeller, Feb 24 2009
A089911(2*a(n)) = 3. - Reinhard Zumkeller, Jul 05 2013
a(n) = 2*(6*n-1) - a(n-1) (with a(0)=2). - Vincenzo Librandi, Nov 20 2010
G.f.: 2*(1+2*x)/(1-x)^2. - Colin Barker, Jan 08 2012
a(n) = (3 * A016813(n) + 1) / 2.- Fred Daniel Kline, Jan 20 2017
a(n) = A016789(A005843(n)). - Felix Fröhlich, Jan 20 2017
Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/18 + log(2)/6. - Amiram Eldar, Dec 10 2021
a(n) = 2 * A016777(n). - Alois P. Heinz, Dec 27 2023
From Elmo R. Oliveira, Mar 08 2024: (Start)
a(n) = 2*a(n-1) - a(n-2) for n >= 2.
E.g.f.: 2*exp(x)*(1 + 3*x). (End)

A039771 Numbers k such that phi(k) is a perfect cube.

Original entry on oeis.org

1, 2, 15, 16, 20, 24, 30, 85, 128, 136, 160, 170, 192, 204, 240, 247, 259, 327, 333, 351, 399, 405, 436, 494, 518, 532, 648, 654, 666, 684, 702, 756, 771, 798, 810, 1024, 1028, 1088, 1111, 1255, 1280, 1360, 1375, 1536, 1542, 1632, 1843, 1853, 1875, 1920, 2008

Offset: 1

Olivier Gérard

a(n) is prime only for a(2)=2, for other cases: eulerphi(p) = p-1 = n^3, and p = 1 + n^3 = (n+1)(n^2-n+1), so p cannot be a prime. - Enrique Pérez Herrero, Aug 29 2010

A013730 is a subsequence. - Enrique Pérez Herrero, Aug 29 2010

			phi(247) = 216 = 6*6*6.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from E. Pérez Herrero)

Cf. A000010, A007614, A039770, A216412.

q:= n-> (c-> iroot(c, 3)^3=c)(numtheory[phi](n)):
select(q, [$1..2200])[];  # Alois P. Heinz, Sep 01 2025

Select[ Range[ 2000 ], IntegerQ[ Power[ EulerPhi[ # ], 1/3 ] ]& ]

for(n=1,1e4,if(ispower(eulerphi(n),3),print1(n", "))) \\ Charles R Greathouse IV, Jul 31 2011

A013731 a(n) = 2^(3*n+2).

Original entry on oeis.org

4, 32, 256, 2048, 16384, 131072, 1048576, 8388608, 67108864, 536870912, 4294967296, 34359738368, 274877906944, 2199023255552, 17592186044416, 140737488355328, 1125899906842624, 9007199254740992, 72057594037927936, 576460752303423488, 4611686018427387904

Offset: 0

N. J. A. Sloane

Starting rank of the (j-1)-Washtenaw series for the fixed ratio 2^(-j-1) (see Griess). - J. Taylor (jt_cpp(AT)yahoo.com), Apr 03 2004
1/4 + 1/32 + 1/256 + 1/2048 + ... = 2/7. - Gary W. Adamson, Aug 29 2008
Independence number of the (n+1)-Sierpinski carpet graph. - Eric W. Weisstein, Sep 06 2017
Clique covering number of the (n+1)-Sierpinski carpet graph. - Eric W. Weisstein, Apr 22 2019

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Robert L. Griess Jr. Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices, arXiv:math/0403480 [math.GR], Mar 28 2004. See Definition 14.21.
Tanya Khovanova, Recursive Sequences
Eric Weisstein's World of Mathematics, Clique Covering Number
Eric Weisstein's World of Mathematics, Independence Number
Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph
Index to divisibility sequences
Index entries for linear recurrences with constant coefficients, signature (8).

Cf. A001018, A013730, A198852.

Cf. A092811 (same sequence with 1 prepended).

[2^(3*n+2): n in [0..20]]; // Vincenzo Librandi, Jun 26 2011

seq(2^(3*n+2),n=0..19); # Nathaniel Johnston, Jun 26 2011

(* Start from Eric W. Weisstein, Sep 06 2017 *)
Table[2^(3 n + 2), {n, 0, 20}]
2^(3 Range[0, 20] + 2)
LinearRecurrence[{8}, {4}, 20]
CoefficientList[Series[-(4/(-1 + 8 x)), {x, 0, 20}], x]
(* End *)

a(n)=4<<(3*n) \\ Charles R Greathouse IV, Apr 07 2012

[lucas_number1(3*n, 2, 0) for n in range(1, 20)] # Zerinvary Lajos, Oct 27 2009

From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 8*a(n-1), n > 0; a(0)=4.
G.f.: 4/(1-8x). (End)
a(n) = A198852(n) + 1. - Michel Marcus, Aug 23 2013
a(n) = A092811(n+1). - Eric W. Weisstein, Sep 06 2017
a(n) = 4*A001018(n). - R. J. Mathar, May 21 2024
E.g.f.: 4*exp(8*x). - Stefano Spezia, May 29 2024

A157176 a(n+1) = a(n - n mod 2) + a(n - n mod 3), a(0) = 1.

Original entry on oeis.org

1, 2, 2, 3, 5, 8, 8, 16, 16, 24, 40, 64, 64, 128, 128, 192, 320, 512, 512, 1024, 1024, 1536, 2560, 4096, 4096, 8192, 8192, 12288, 20480, 32768, 32768, 65536, 65536, 98304, 163840, 262144, 262144, 524288, 524288, 786432, 1310720, 2097152, 2097152, 4194304, 4194304

Offset: 0

Reinhard Zumkeller, Feb 24 2009

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,8).

Cf. A001018, A008588, A013730, A016921, A016933, A016945, A016957, A016969, A067412, A103333.

LinearRecurrence[{0,0,0,0,0,8},{1, 2, 2, 3, 5, 8},45] (* Stefano Spezia, May 29 2024 *)

a(n+6) = 8*a(n).
a(6*k) = 8^k; a(A008588(n))=A001018(n);
a(6*k+1) = a(6*k+2) = 2*8^k; a(A016921(n))=a(A016933(n))=A013730(n);
a(6*k+3) = 3*8^k; a(A016945(n))=A103333(n+1);
a(6*k+4) = 5*8^k; a(A016957(n))=A067412(n+1);
a(6*k+5) = 8^(k+1); a(A016969(n))=A001018(n+1).
G.f.: (1 + 2*x + 2*x^2 + 3*x^3 + 5*x^4 + 8*x^5)/((1 - 2*x^2)*(1 + 2*x^2 + 4*x^4)). - Stefano Spezia, May 29 2024

a(43)-a(44) from Stefano Spezia, May 29 2024

A013732 a(n) = 3^(3*n + 1).

Original entry on oeis.org

3, 81, 2187, 59049, 1594323, 43046721, 1162261467, 31381059609, 847288609443, 22876792454961, 617673396283947, 16677181699666569, 450283905890997363, 12157665459056928801, 328256967394537077627, 8862938119652501095929

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (27).

Cf. A013730, A013733, A013734.

[3^(3*n+1): n in [0..25]]; // Vincenzo Librandi, May 25 2011

seq(3^(3*n+1),n=0..15); # Nathaniel Johnston, Jun 26 2011

NestList[27#&,3,20] (* Harvey P. Dale, Apr 01 2018 *)

a(n)=3^(3*n+1) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 25 2008: (Start)
a(n) = 27*a(n-1); a(0)=3.
G.f.: 3/(1-27*x). (End)

A132024 Decimal expansion of Product_{k>=0} (1-1/(2*8^k)).

Original entry on oeis.org

4, 6, 4, 5, 6, 8, 8, 8, 3, 6, 8, 6, 4, 7, 6, 3, 9, 0, 9, 8, 1, 9, 5, 9, 5, 6, 9, 7, 4, 8, 4, 7, 8, 0, 1, 0, 8, 7, 0, 0, 5, 8, 5, 1, 5, 4, 9, 5, 1, 2, 3, 0, 6, 5, 5, 6, 6, 0, 8, 5, 6, 0, 5, 9, 7, 0, 6, 0, 9, 9, 5, 7, 6, 2, 7, 4, 4, 1, 5, 4, 3, 8, 4, 8, 7, 8, 8, 8, 1, 2, 5, 0, 7, 6, 2, 1, 9, 4, 7, 0, 8, 1, 7

Offset: 0

Hieronymus Fischer, Aug 14 2007

			0.46456888368647639098...

Cf. A048651, A098844, A067080, A132019, A132026, A132032, A132036, A000217, A013730.

RealDigits[QPochhammer[1/2,1/8],10,120][[1]] (* Harvey P. Dale, May 23 2011 *)

prodinf(k=0, 1 - 1/(2*8^k)) \\ Amiram Eldar, May 09 2023

Equals lim inf_{n->oo} Product_{k=0..floor(log_8(n))} floor(n/8^k)*8^k/n.
Equals lim inf_{n->oo} A132032(n)/n^(1+floor(log_8(n)))*8^(1/2*(1+floor(log_8(n)))*floor(log_8(n))).
Equals lim inf_{n->oo} A132032(n)/n^(1+floor(log_8(n)))*8^A000217(floor(log_8(n))).
Equals (1/2)*exp(-Sum_{n>0} 8^(-n)*Sum_{k|n} 1/(k*2^k)).
Equals lim inf_{n->oo} A132032(n)/A132032(n+1).
Equals Product_{n>=0} (1 - 1/A013730(n)). - Amiram Eldar, May 09 2023

Name corrected by Amiram Eldar, May 09 2023

A013746 a(n) = 10^(3*n + 1).

Original entry on oeis.org

10, 10000, 10000000, 10000000000, 10000000000000, 10000000000000000, 10000000000000000000, 10000000000000000000000, 10000000000000000000000000, 10000000000000000000000000000, 10000000000000000000000000000000, 10000000000000000000000000000000000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (1000).

Subsequence of A011557 (10^n).

Cf. A013730, A013736, A013747, A016777.

[10^(3*n+1): n in [0..15]]; // Vincenzo Librandi, Jun 26 2011

10^(3Range[0,10]+1)  (* Harvey P. Dale, Mar 28 2011 *)

a(n)=10^(3*n+1) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 30 2008: (Start)
a(n) = 1000*a(n-1); a(0)=10.
G.f.: 10/(1-1000*x). (End)
From Elmo R. Oliveira, Jul 07 2025: (Start)
E.g.f.: 10*exp(1000*x).
a(n) = A013747(n)/10 = A013730(n)*A013736(n) = A011557(A016777(n)). (End)

A359987 Number of edge cuts in the n-ladder graph P_2 X P_n.

Original entry on oeis.org

1, 11, 105, 919, 7713, 63351, 514321, 4148839, 33347041, 267489431, 2143168305, 17160184519, 137349160833, 1099102033911, 8794224638161, 70360221445159, 562911076526881, 4503422288363351, 36027988077717105, 288226686123491719, 2305826176955087553, 18446667292472959671

Offset: 1

Andrew Howroyd, Jan 28 2023

Andrew Howroyd, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Edge Cut.
Eric Weisstein's World of Mathematics, Ladder Graph.
Index entries for linear recurrences with constant coefficients, signature (13,-42,16).

Row 2 of A359990.
Cf. A013730, A107839, A356828 (vertex cuts), A359989.
Cf. A359621, A359622.

LinearRecurrence[{13, -42, 16}, {1, 11, 105}, 25] (* Paolo Xausa, Jun 24 2024 *)
Table[2^(3 n - 2) + (((5 - Sqrt[17])/2)^n - ((5 + Sqrt[17])/2)^n)/Sqrt[17], {n, 20}] // Expand (* Eric W. Weisstein, Nov 03 2024 *)
CoefficientList[Series[-(1 - 2 x + 4 x^2)/((-1 + 8 x) (1 - 5 x + 2 x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Nov 03 2024 *)

Vec((1 - 2*x + 4*x^2)/((1 - 8*x)*(1 - 5*x + 2*x^2)) + O(x^25))

a(n) = 13*a(n-1) - 42*a(n-2) + 16*a(n-3) for n > 3.
a(n) = A013730(n-1) - A107839(n-1).
G.f.: x*(1 - 2*x + 4*x^2)/((1 - 8*x)*(1 - 5*x + 2*x^2)).

cp's OEIS Frontend

A016921 a(n) = 6*n + 1.

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A001018 Powers of 8: a(n) = 8^n.

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A016933 a(n) = 6*n + 2.

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A039771 Numbers k such that phi(k) is a perfect cube.

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A013731 a(n) = 2^(3*n+2).

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A157176 a(n+1) = a(n - n mod 2) + a(n - n mod 3), a(0) = 1.

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