A015503 a(1) = 1, a(n) = Sum_{k=1..n-1} ((4^k - 1)/3)*a(k).

1, 1, 6, 132, 11352, 3882384, 5303336544, 28966824203328, 632809241545903488, 55296137144764138588416, 19327437631660830304254690816, 27021729207700270170039091739231232, 151116480551518237100547636877027177224192

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..50

Crossrefs

Sequences with the recurrence a(n) = (m^(n-1) + m-2)*a(n-1)/(m-1): A036442 (m=2), A015502 (m=3), this sequence (m=4), A015506 (m=5), A015507 (m=6), A015508 (m=7), A015509 (m=8), A015511 (m=9), A015512 (m=10), A015513 (m=11), A015515 (m=12).

Programs

Magma

[n le 2 select 1 else ((4^(n-1)+2)/3)*Self(n-1): n in [1..15]]; // Vincenzo Librandi, Nov 11 2012

Mathematica

a[n_, m_]:= a[n, m]= If[n<3, 1, (m^(n-1)+m-2)*a[n-1,m]/(m-1)];
Table[a[n,4], {n,30}] (* G. C. Greubel, Apr 29 2023 *)

SageMath

@CachedFunction # a = A015503
def a(n,m): return 1 if (n<3) else (m^(n-1) + m-2)*a(n-1,m)/(m-1)
[a(n,4) for n in range(1,31)] # G. C. Greubel, Apr 29 2023

Formula

a(n) = ((4^(n-1) + 2)/3) * a(n-1). - Vincenzo Librandi, Nov 11 2012