A387869 - OEIS

A387869

a(n) = Sum_{k=0..n} binomial(2*n+1,4*k).

1, 1, 6, 36, 136, 496, 2016, 8256, 32896, 130816, 523776, 2098176, 8390656, 33550336, 134209536, 536887296, 2147516416, 8589869056, 34359607296, 137439215616, 549756338176, 2199022206976, 8796090925056, 35184376283136, 140737496743936, 562949936644096

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..700

Index entries for linear recurrences with constant coefficients, signature (4,-4,16).

FORMULA

G.f.: (1-3*x+6*x^2)/((1-4*x) * (1+4*x^2)).

a(n) = 4*a(n-1) - 4*a(n-2) + 16*a(n-3) for n > 2.

a(2*n) = A090407(n), a(2*n+1) = A090408(n).

a(n) = 2^(2*n-1) + (-1)^floor((n+1)/2)*2^(n-1).

MATHEMATICA