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A097081 Sum C(n,4k)2^k, k = 0 . . n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..31.

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

FORMULA

G.f. : (1-x)^3/((1-x)^4-2x^4); a(n)=sum{k=0..floor(n/2), binomial(n, 4k)2^k }; a(n)=4a(n-1)-6a(n-2)+4a(n-3)+a(n-4).

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 *)

CROSSREFS

Cf. A093406.

Sequence in context: A277049 A261148 A071568 * A093406 A107587 A245931

Adjacent sequences:  A097078 A097079 A097080 * A097082 A097083 A097084

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 23 2004

STATUS

approved

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Last modified October 20 16:12 EDT 2019. Contains 328268 sequences. (Running on oeis4.)