A097114 Expansion of (1 + 8x - 42x^2 - 392x^3)/(1 - 99x^2 + 2450x^4).

1, 8, 57, 400, 3193, 20000, 176457, 1000000, 9646393, 50000000, 522673257, 2500000000, 28110989593, 125000000000, 1502438490057, 6250000000000, 79869486012793, 312500000000000, 4226104814626857, 15625000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (0,99,0,-2450).

Formula

G.f.: 8*(1+x)/(1-50*x^2)-7/(1-49*x^2);

a(n) = 99*a(n-2) - 2450*a(n-4);

a(n) = (4 + 2*sqrt(50)/25)*(sqrt(50))^n + (4 - 2*sqrt(50)/25)*(-sqrt(50))^n - 7^(n+1)*(1 + (-1)^n)/2;

a(n) = Sum_{k=0..n} binomial(floor(n/2), floor(k/2))*7^k.

Crossrefs

Sequence in context: A297369 A023000 A331792 * A022038 A277671 A015453

Adjacent sequences: A097111 A097112 A097113 * A097115 A097116 A097117

Keyword

easy,nonn

Author

Paul Barry, Jul 25 2004

Status

approved