A097113 Expansion of (1 + 5*x - 12*x^2 - 80*x^3)/(1 - 33*x^2 + 272*x^4).

1, 5, 21, 85, 421, 1445, 8181, 24565, 155461, 417605, 2904981, 7099285, 53578981, 120687845, 977951541, 2051693365, 17698918021, 34878787205, 318061475541, 592939382485, 5681922991141, 10079969502245, 100990737360501

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (0,33,0,-272).

Formula

G.f.: 5*(1+x)/(1-17*x^2) - 4/(1-16*x^2).

a(n) = 33*a(n-2) - 272*a(n-4).

a(n) = (5/2 + 5*sqrt(17)/34)*(sqrt(17))^n + (5/2 - 5*sqrt(17)/34)*(-sqrt(17))^n - 4^(n+1)*(1+(-1)^n)/2.

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

Mathematica

CoefficientList[Series[(1+5x-12x^2-80x^3)/(1-33x^2+272x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{0, 33, 0, -272}, {1, 5, 21, 85}, 30] (* Harvey P. Dale, Jul 19 2011 *)

Crossrefs

Sequence in context: A026855 A272832 A273489 * A368345 A265939 A012814

Adjacent sequences: A097110 A097111 A097112 * A097114 A097115 A097116

Keyword

easy,nonn

Author

Paul Barry, Jul 25 2004

Status

approved