A097081 a(n) = Sum_{k=0..n} C(n,4k)*2^k.

1, 1, 1, 1, 3, 11, 31, 71, 145, 289, 601, 1321, 2979, 6683, 14743, 32111, 69697, 151777, 332113, 728689, 1598883, 3503627, 7668079, 16774775, 36704017, 80343361, 175916521, 385196761, 843365379, 1846290395, 4041672871, 8847607391

Offset: 0

Author

Paul Barry, Jul 23 2004

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,1).

Crossrefs

Cf. A093406.

Programs

Mathematica

Table[Sum[Binomial[n,4k]2^k,{k,0,n}],{n,0,40}] (* or *) LinearRecurrence[ {4,-6,4,1},{1,1,1,1},40] (* Harvey P. Dale, Feb 26 2012 *)

Formula

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

a(n) = Sum_{k=0..floor(n/2)} binomial(n,4*k)*2^k;

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)+a(n-4).