A013731 -id:A013731 - cp's OEIS frontend

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

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)

A013730 a(n) = 2^(3*n+1).

Original entry on oeis.org

2, 16, 128, 1024, 8192, 65536, 524288, 4194304, 33554432, 268435456, 2147483648, 17179869184, 137438953472, 1099511627776, 8796093022208, 70368744177664, 562949953421312, 4503599627370496, 36028797018963968, 288230376151711744, 2305843009213693952, 18446744073709551616

Offset: 0

N. J. A. Sloane

1/2 + 1/16 + 1/128 + 1/1024 + ... = 4/7. - Gary W. Adamson, Aug 29 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (8).
Index to divisibility sequences.

Cf. A013731, A016921, A016933, A132024, A157176.

[2^(3*n+1): n in [0..30]]; // Vincenzo Librandi, May 04 2011

seq(2^(3*n+1),n=0..19); # Nathaniel Johnston, Jun 26 2011

Table[2^n, {n, 1, 100, 3}] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
2^(3 Range[0, 40] + 1) (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
Table[2^(3 n + 1), {n, 0, 20}] (* Eric W. Weisstein, Nov 03 2024 *)
2^(3 Range[0, 20] + 1) (* Eric W. Weisstein, Nov 03 2024 *)
2^Range[1, 61, 3] (* Eric W. Weisstein, Nov 03 2024 *)
LinearRecurrence[{8}, {2}, 20] (* Eric W. Weisstein, Nov 03 2024 *)
CoefficientList[Series[2/(1 - 8 x), {x, 0, 20}], x] (* Eric W. Weisstein, Nov 03 2024 *)

a(n)=2<<(3*n) \\ Charles R Greathouse IV, Jun 14 2011

From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 8*a(n-1), n > 0; a(0)=2.
G.f.: 2/(1-8x). (End)
a(n) = A157176(A016921(n)) = A157176(A016933(n)). - Reinhard Zumkeller, Feb 24 2009
From Amiram Eldar, May 08 2023: (Start)
Sum_{n>=0} (-1)^n/a(n) = 4/9.
Product_{n>=0} (1 - 1/a(n)) = A132024. (End)
E.g.f.: 2*exp(8*x). - Stefano Spezia, May 29 2024

A088138 Generalized Gaussian Fibonacci integers.

Original entry on oeis.org

0, 1, 2, 0, -8, -16, 0, 64, 128, 0, -512, -1024, 0, 4096, 8192, 0, -32768, -65536, 0, 262144, 524288, 0, -2097152, -4194304, 0, 16777216, 33554432, 0, -134217728, -268435456, 0, 1073741824, 2147483648, 0, -8589934592, -17179869184, 0, 68719476736, 137438953472

Offset: 0

Paul Barry, Sep 20 2003

The sequence 0,1,-2,0,8,-16,... has g.f. x/(1+2*x-4*x^2), a(n) = 2^n*sin(2n*Pi/3)/sqrt(3) and is the inverse binomial transform of sin(sqrt(3)*x)/sqrt(3): 0,1,-3,0,9,...
a(n+1) is the Hankel transform of A100192. - Paul Barry, Jan 11 2007
a(n+1) is the trinomial transform of A010892: a(n+1) = Sum_{k=0..2n} trinomial(n,k)*A010892(k+1) where trinomial(n, k) = trinomial coefficients (A027907). - Paul Barry, Sep 10 2007
a(n+1) is the Hankel transform of A100067. - Paul Barry, Jun 16 2009
From Paul Curtz, Oct 04 2009: (Start)
1) a(n) = A131577(n)*A128834(n).
2) Binomial transform of 0,1,0,-3,0,9,0,-27, see A000244.
3) Sequence is identical to every 2n-th difference divided by (-3)^n.
4) a(3n) + a(3n+1) + a(3n+2) = (-1)^n*3*A001018(n) for n >= 1.
5) For missing terms in a(n) see A013731 = 4*A001018. (End)
The coefficient of i of Q^n, where Q is the quaternion 1+i+j+k. Due to symmetry, also the coefficients of j and of k. - Stanislav Sykora, Jun 11 2012 [The coefficients of 1 are in A138230. - Wolfdieter Lang, Jan 28 2016]
With different signs, 0, 1, -2, 0, 8, -16, 0, 64, -128, 0, 512, -1024, ... is the Lucas U(-2,4) sequence. - R. J. Mathar, Jan 08 2013

Robert Israel, Table of n, a(n) for n = 0..3300
Beata Bajorska-Harapińska, Barbara Smoleń, and Roman Wituła, On Quaternion Equivalents for Quasi-Fibonacci Numbers, Shortly Quaternaccis, Advances in Applied Clifford Algebras (2019) Vol. 29, 54.
Wikipedia, Lucas sequence
Index entries for linear recurrences with constant coefficients, signature (2,-4).
Index entries for Lucas sequences

Cf. A084102, A088137, A045873, A088139, A138230.

a:=[0,1];; for n in [3..40] do a[n]:=2*a[n-1]-4*a[n-2]; od; a; # Muniru A Asiru, Oct 23 2018

I:=[0,1]; [n le 2 select I[n] else 2*Self(n-1) - 4*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 15 2018

M:= <<1+I,1+I>|>:
T:= <<-I/2,0>|<0,I/2>>:
seq(LinearAlgebra:-Trace(T.M^n),n=0..100); # Robert Israel, Jan 28 2016

Join[{a=0,b=1},Table[c=2*b-4*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)
LinearRecurrence[{2, -4}, {0, 1}, 40] (* Vincenzo Librandi, Jan 29 2016 *)
Table[2^(n-2)*((-1)^Quotient[n-1,3]+(-1)^Quotient[n,3]), {n,0,40}] (*Federico Provvedi,Apr 24 2022*)

/* lists powers of any quaternion */
QuaternionToN(a,b,c,d,nmax) = {local (C);C = matrix(nmax+1,4);C[1,1]=1;for(n=2,nmax+1,C[n,1]=a*C[n-1,1]-b*C[n-1,2]-c*C[n-1,3]-d*C[n-1,4];C[n,2]=b*C[n-1,1]+a*C[n-1,2]+d*C[n-1,3]-c*C[n-1,4];C[n,3]=c*C[n-1,1]-d*C[n-1,2]+a*C[n-1,3]+b*C[n-1,4];C[n,4]=d*C[n-1,1]+c*C[n-1,2]-b*C[n-1,3]+a*C[n-1,4];);return (C);} /* Stanislav Sykora, Jun 11 2012 */

my(x='x+O('x^30)); concat([0], Vec(x/(1-2*x+4*x^2))) \\ G. C. Greubel, Oct 22 2018

a(n) = 2^(n-1)*polchebyshev(n-1, 2, 1/2); \\ Michel Marcus, May 02 2022

[lucas_number1(n,2,4) for n in range(0, 39)] # Zerinvary Lajos, Apr 23 2009

G.f.: x/(1-2*x+4*x^2).
E.g.f.: exp(x)*sin(sqrt(3)*x)/sqrt(3).
a(n) = 2*a(n-1) - 4*a(n-2), a(0)=0, a(1)=1.
a(n) = ((1+i*sqrt(3))^n - (1-i*sqrt(3))^n)/(2*i*sqrt(3)).
a(n) = Im( (1+i*sqrt(3))^n/sqrt(3) ).
a(n) = Sum_{k=0..floor(n/2)} C(n, 2*k+1)*(-3)^k.
From Paul Curtz, Oct 04 2009: (Start)
a(n) = a(n-1) + a(n-2) + 2*a(n-3).
a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3).
a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4). (End)
E.g.f.: exp(x)*sin(sqrt(3)*x)/sqrt(3) = G(0)*x^2 where G(k)= 1 + (3*k+2)/(2*x - 32*x^5/(16*x^4 - 3*(k+1)*(3*k+2)*(3*k+4)*(3*k+5)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jul 26 2012
G.f.: x/(1-2*x+4*x^2) = 2*x^2*G(0) where G(k)= 1 + 1/(2*x - 32*x^5/(16*x^4 - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jul 27 2012
a(n) = -2^(n-1)*Product_{k=1..n}(1 + 2*cos(k*Pi/n)) for n >= 1. - Peter Luschny, Nov 28 2019
a(n) = 2^(n-1) * U(n-1, 1/2), where U(n, x) is the Chebyshev polynomial of the second kind. - Federico Provvedi, Apr 24 2022

A013733 a(n) = 3^(3n+2).

Original entry on oeis.org

9, 243, 6561, 177147, 4782969, 129140163, 3486784401, 94143178827, 2541865828329, 68630377364883, 1853020188851841, 50031545098999707, 1350851717672992089, 36472996377170786403, 984770902183611232881, 26588814358957503287787

Offset: 0

N. J. A. Sloane

Additive digital root of a(n) is equal to 9. - Miquel Cerda, Oct 31 2016

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. A013731, A013732, A013735, A013737.

[3^(3*n+2): n in [0..25]]; // Vincenzo Librandi, May 25 2011

seq(3^(3*n+2),n=0..15); # Nathaniel Johnston, Jun 26 2011

Table[3^(3n+2), {n,0,100}] (* Wesley Ivan Hurt, Oct 24 2013 *)

a(n)=3^(3*n+2) \\ Charles R Greathouse IV, Jul 11 2016

a(n)=27*a(n-1), n>0 ; a(0)=9 . G.f.: 9/(1-27*x). - Philippe Deléham, Nov 25 2008

A365801 Numbers k such that A163511(k) is a cube.

Original entry on oeis.org

0, 4, 9, 19, 32, 39, 65, 72, 79, 131, 145, 152, 159, 256, 263, 291, 305, 312, 319, 513, 520, 527, 576, 583, 611, 625, 632, 639, 1027, 1041, 1048, 1055, 1153, 1160, 1167, 1216, 1223, 1251, 1265, 1272, 1279, 2048, 2055, 2083, 2097, 2104, 2111, 2307, 2321, 2328, 2335, 2433, 2440, 2447, 2496, 2503, 2531, 2545, 2552

Offset: 1

Antti Karttunen, Oct 01 2023

nonn

The sequence is defined inductively as:
 (a) it contains 0 and 4,
   and
 (b) for any nonzero term a(n), (2*a(n)) + 1 and 8*a(n) are also included as terms.
Because the inductive definition guarantees that all terms after 0 are of the form 7k+2, 7k+4 or 7k+5 (A047378), and because for any n >= 0, n^3 == 0, 1 or 6 (mod 7), (i.e., cubes are in A047275), it follows that there are no cubes in this sequence after the initial 0.

Positions of multiples of 3 in A365805.
Sequence A243071(n^3), n >= 1, sorted into ascending order.
Subsequence of A047378 (after the initial 0).
Subsequences: A013731, A153894.
Cf. A000578, A047275, A163511.
Cf. also A365802, A365808.

A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
isA365801(n) = ispower(A163511(n),3);

isA365801(n) = if(n<=4, !(n%4), if(n%2, isA365801((n-1)/2), if(n%8, 0, isA365801(n/8))));

A092811 Expansion of g.f. (1-4x)/(1-8x).

Original entry on oeis.org

1, 4, 32, 256, 2048, 16384, 131072, 1048576, 8388608, 67108864, 536870912, 4294967296, 34359738368, 274877906944, 2199023255552, 17592186044416, 140737488355328, 1125899906842624, 9007199254740992, 72057594037927936, 576460752303423488, 4611686018427387904

Offset: 0

Paul Barry, Mar 10 2004

4th binomial transform of (1,0,16,0,256,...).

Number of compositions of even natural numbers into n parts <= 7. - Adi Dani, May 28 2011

			From _Adi Dani_, May 28 2011: (Start)
a(2)=32: there are 32 compositions of even natural numbers into 2 parts <= 7:
(0,0);
(0,2),(2,0),(1,1);
(0,4),(4,0),(1,3),(3,1),(2,2);
(0,6),(6,0),(1,5),(5,1),(2,4),(4,2),(3,3);
(1,7),(7,1),(2,6),(6,2),(3,5),(5,3),(4,4);
(3,7),(7,3),(4,6),(6,4),(5,5);
(5,7),(7,5),(6,6);
(7,7).  (End)

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index to divisibility sequences
Index entries for linear recurrences with constant coefficients, signature (8).

Cf. A001045, A013731 (same sequence omitting initial 1), A055372, A134309.

[8^n/2+0^n/2: n in [0..20]]; // Vincenzo Librandi, Jun 16 2011

Table[EulerPhi[8^n],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Nov 10 2009 *)

a(n)=max(1,8^n/2) \\ Charles R Greathouse IV, Apr 09 2012

def A092811(n): return 1<<3*n-1 if n else 1 # Chai Wah Wu, Apr 25 2025

a(n) = 8^n/2 + 0^n/2.
a(n) = A001045(3n+1) - A001045(3n-1) + 0^n/2.
a(n) = A013731(n-1), n > 0. - R. J. Mathar, Sep 08 2008
a(n) = 4 * 8^(n-1), a(0)=1. - Vincenzo Librandi, Jun 16 2011
a(n) = Sum_{k=0..n} A134309(n,k)*4^k = Sum_{k=0..n} A055372(n,k)*3^k. - Philippe Deléham, Feb 04 2012
E.g.f.: (1 + exp(8*x))/2. - Stefano Spezia, May 29 2024

A013747 a(n) = 10^(3*n + 2).

Original entry on oeis.org

100, 100000, 100000000, 100000000000, 100000000000000, 100000000000000000, 100000000000000000000, 100000000000000000000000, 100000000000000000000000000, 100000000000000000000000000000, 100000000000000000000000000000000, 100000000000000000000000000000000000

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. A013731, A013737, A013746, A016789.

[10^(3*n+2): n in [0..15]]; // Vincenzo Librandi, Jun 26 2011

a(n)=10^(3*n+2) \\ Charles R Greathouse IV, Jul 10 2016

From Philippe Deléham, Nov 30 2008: (Start)
a(n) = 1000*a(n-1); a(0)=100.
G.f.: 100/(1-1000*x).
a(n) = 10*A013746(n). (End)
From Elmo R. Oliveira, Jul 07 2025: (Start)
E.g.f.: 100*exp(1000*x).
a(n) = A013731(n)*A013737(n) = A011557(A016789(n)). (End)

A114076 Numbers k such that k * phi(k) is a cube.

Original entry on oeis.org

1, 4, 32, 50, 72, 225, 256, 400, 576, 900, 1944, 2048, 2166, 2312, 2646, 3200, 4107, 4563, 4608, 5202, 6075, 6250, 7200, 7225, 15125, 15552, 16384, 16428, 17328, 18252, 18496, 21168, 23762, 24300, 25600, 28125, 28900, 35378, 36864, 41616, 50000, 52488, 57600

Offset: 1

Giovanni Resta, Feb 13 2006

nonn

From Robert Israel, Sep 06 2020: (Start)
If n > 1 is in the sequence, A071178(n) == 2 (mod 3).
If p=2^(2^k)+1 is in A019434, includes 2^a*p^b where a == 2^k-1 (mod 3) and b == 2 (mod 3).
If members m and n are coprime, then m*n is in the sequence.
If n is in the sequence and prime p divides n, then p^3*n is in the sequence. (End)
To look for terms it suffices to see if cubes have a divisors pair (k, m) such that phi(m) = k. - David A. Corneth, May 21 2024

			phi(1944) * 1944 = 1259712 = 108^3.

David A. Corneth, Table of n, a(n) for n = 1..8565 (first 300 terms from Robert Israel, terms <= 5*10^11)
David A. Corneth, PARI program

Aside from the first term, a subsequence of A070003. A013731 is a subsequence.

Cf. A000010, A071178, A019434.

filter:= proc(n) local F;
  F:= ifactors(n*numtheory:-phi(n))[2];
  type(map(t -> t[2]/3, F), list(integer));
end proc:
select(filter, [$1..10^5]); # Robert Israel, Sep 06 2020

Select[Range[57600],IntegerQ[(# EulerPhi[#])^(1/3)]&] (* Stefano Spezia, May 29 2024 *)

isok(n) = ispower(n*eulerphi(n), 3); \\ Michel Marcus, Jan 22 2014

upto(n)= res = List(); forfactored(i = 1, n, if(ispower(i[1] * eulerphi(i[2]), 3), listput(res, i[1]); ) ); res  \\ David A. Corneth, Dec 08 2022

PARI
```
\\ See Corneth link
```

from sympy import integer_nthroot, totient as phi
def ok(k): return integer_nthroot(k * phi(k), 3)[1]
print([k for k in range(1, 60000) if ok(k)]) # Michael S. Branicky, Dec 08 2022

More terms from Michel Marcus, Jan 22 2014

A198852 a(n) = 4*8^n - 1.

Original entry on oeis.org

3, 31, 255, 2047, 16383, 131071, 1048575, 8388607, 67108863, 536870911, 4294967295, 34359738367, 274877906943, 2199023255551, 17592186044415, 140737488355327, 1125899906842623, 9007199254740991, 72057594037927935, 576460752303423487, 4611686018427387903

Offset: 0

Vincenzo Librandi, Oct 31 2011

In base 8, the numbers of this sequence are written 37, 377, 3777, 37777, ... and satisfy the A052148 condition. - Michel Marcus, Aug 23 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-8).

Cf. A013731, A052148.

Magma
```
[4*8^n-1: n in [0..30]];
```

a(n) = 8*a(n-1) + 7.
a(n) = 9*a(n-1) - 8*a(n-2) for n > 1.
G.f.: ( 3+4*x ) / ( (8*x-1)*(x-1) ). - R. J. Mathar, Oct 31 2011
a(n) = A013731(n) - 1. - Michel Marcus, Aug 23 2013
E.g.f.: exp(x)*(4*exp(7*x) - 1). - Stefano Spezia, May 29 2024

A013767 a(n) = 20^(3*n + 2).

Original entry on oeis.org

400, 3200000, 25600000000, 204800000000000, 1638400000000000000, 13107200000000000000000, 104857600000000000000000000, 838860800000000000000000000000, 6710886400000000000000000000000000, 53687091200000000000000000000000000000, 429496729600000000000000000000000000000000

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 (8000).

Subsequence of A009964.

Cf. A013731, A013747, A016789.

[20^(3*n+2): n in [0..10]]; // Vincenzo Librandi, Jun 27 2011

NestList[8000#&,400,10] (* Harvey P. Dale, May 11 2018 *)

a(n)=20^(3*n+2) \\ Charles R Greathouse IV, Jul 10 2016

From Elmo R. Oliveira, Feb 27 2025: (Start)
G.f.: 400/(1 - 8000*x).
E.g.f.: 400*exp(8000*x).
a(n) = A013731(n)*A013747(n) = A009964(A016789(n)). (End)

cp's OEIS Frontend

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

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A013730 a(n) = 2^(3*n+1).

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A088138 Generalized Gaussian Fibonacci integers.

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A013733 a(n) = 3^(3n+2).

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A365801 Numbers k such that A163511(k) is a cube.

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A092811 Expansion of g.f. (1-4*x)/(1-8*x).

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A092811 Expansion of g.f. (1-4x)/(1-8x).