A090408 a(n) = Sum_{k=0..n} binomial(4n+3,4k).

1, 36, 496, 8256, 130816, 2098176, 33550336, 536887296, 8589869056, 137439215616, 2199022206976, 35184376283136, 562949936644096, 9007199321849856, 144115187807420416, 2305843010287435776, 36893488143124135936, 590295810375885520896, 9444732965670570950656

Offset: 0

Author

Paul Barry, Nov 29 2003

Keywords

• easy
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (12,64).

Crossrefs

Cf. A070775, A001025, A090407, A038503.

Programs

Mathematica

Table[Sum[Binomial[4n+3,4k],{k,0,n}],{n,0,20}] (* Harvey P. Dale, Feb 12 2020 *)

Formula

a(n) = 2^(1+4*n) - (-1)^n*4^n. - R. J. Mathar, Nov 27 2014