A096882 Expansion of g.f. (1 + 7*x)/(1 - 50*x^2).

1, 7, 50, 350, 2500, 17500, 125000, 875000, 6250000, 43750000, 312500000, 2187500000, 15625000000, 109375000000, 781250000000, 5468750000000, 39062500000000, 273437500000000, 1953125000000000, 13671875000000000, 97656250000000000, 683593750000000000, 4882812500000000000

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,50).

Formula

a(n) = 6*a(n-1) + 7*a(n-2) + 50^floor((n-2)/2).

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

E.g.f.: cosh(5*sqrt(2)*x) + 7*sinh(5*sqrt(2)*x)/(5*sqrt(2)). - Stefano Spezia, Mar 31 2023

Mathematica

a[n_]:=Sum[Binomial[Floor[n/2], k]7^(n-2k), {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* Stefano Spezia, Mar 31 2023 *)
LinearRecurrence[{0, 50}, {1, 7}, 30] (* Harvey P. Dale, Sep 20 2024 *)

Crossrefs

Cf. A004663, A026383, A016116, A096881.

Sequence in context: A266360 A288787 A033117 * A033125 A022037 A054413

Adjacent sequences: A096879 A096880 A096881 * A096883 A096884 A096885

Keyword

easy,nonn

Author

Paul Barry, Jul 14 2004

Extensions

More terms from Stefano Spezia, Mar 31 2023

Status

approved