A013823 -id:A013823 - cp's OEIS frontend

A013824 a(n) = 2^(5*n + 3).

8, 256, 8192, 262144, 8388608, 268435456, 8589934592, 274877906944, 8796093022208, 281474976710656, 9007199254740992, 288230376151711744, 9223372036854775808, 295147905179352825856, 9444732965739290427392, 302231454903657293676544, 9671406556917033397649408

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 (32).

Cf. A000079 (2^n), A009976, A013822, A013823, A016885 (5*n+3).

[2^(5*n+3): n in [0..15]]; // Vincenzo Librandi, Jul 07 2011

2^(5*Range[0, 20] + 3) (* Paolo Xausa, Feb 21 2025 *)

a(n)=2^(5*n+3) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 24 2008: (Start)
a(n) = 32*a(n-1), n > 0; a(0)=8.
G.f.: 8/(1-32*x).
a(n) = 8*A009976(n). (End)
From Elmo R. Oliveira, Feb 20 2025: (Start)
E.g.f.: 8*exp(32*x).
a(n) = A000079(A016885(n)). (End)
a(n) = 2*A013823(n) = 4*A013822(n). - Paolo Xausa, Feb 21 2025

A359988 Number of edge cuts in the 3 X n grid graph.

Original entry on oeis.org

3, 105, 3665, 123215, 4051679, 131630449, 4248037953, 136587740399, 4382607093471, 140457446235441, 4498520188148993, 144023056568886959, 4610014925578108703, 147543642097619999089, 4721816707356538941633, 151105755554498621737583, 4835522406931884652356447

Offset: 1

Andrew Howroyd, Jan 28 2023

Andrew Howroyd, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (54,-777,2390,-1736,256).

Row 3 of A359990.

Cf. A013823, A158453, A359987.

Vec((3 - 57*x + 326*x^2 - 280*x^3 + 32*x^4)/((1 - 32*x)*(1 - 22*x + 73*x^2 - 54*x^3 + 8*x^4)) + O(x^20))

a(n) = 54*a(n-1) - 777*a(n-2) + 2390*a(n-3) - 1736*a(n-4) + 256*a(n-5) for n > 5.
G.f.: x*(3 - 57*x + 326*x^2 - 280*x^3 + 32*x^4)/((1 - 32*x)*(1 - 22*x + 73*x^2 - 54*x^3 + 8*x^4)).
a(n) = A013823(n-1) - A158453(n).

A013895 a(n) = 20^(5*n + 2).

Original entry on oeis.org

400, 1280000000, 4096000000000000, 13107200000000000000000, 41943040000000000000000000000, 134217728000000000000000000000000000, 429496729600000000000000000000000000000000, 1374389534720000000000000000000000000000000000000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (3200000).

Subsequence of A009964.

Cf. A013823, A013855, A013894, A013896, A016873.

[20^(5*n+2): n in [0..10]]; // Vincenzo Librandi, May 27 2011

A013895:=n->20^(5*n+2): seq(A013895(n), n=0..10); # Wesley Ivan Hurt, Nov 17 2015

20^(5 Range[0, 10] + 2) (* or *) CoefficientList[Series[-400/(3200000*x - 1), {x, 0, 10}], x] (* Wesley Ivan Hurt, Nov 17 2015 *)

Vec(-400/(3200000*x-1) + O(x^10)) \\ Colin Barker, Nov 17 2015

a(n) = 3200000*a(n-1), a(0)=400. - Vincenzo Librandi, May 27 2011
G.f.: -400/(3200000*x-1). - Colin Barker, Nov 17 2015
a(n) = A009964(A016873(n)). - Wesley Ivan Hurt, Nov 17 2015
From Elmo R. Oliveira, Jul 13 2025: (Start)
E.g.f.: 400*exp(3200000*x).
a(n) = 20*A013894(n) = A013896(n)/20 = A013823(n)*A013855(n). (End)

cp's OEIS Frontend

A013824 a(n) = 2^(5*n + 3).

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A359988 Number of edge cuts in the 3 X n grid graph.

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A013895 a(n) = 20^(5*n + 2).

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