A096881 Expansion of g.f. (1 + 4*x)/(1 - 17*x^2).

1, 4, 17, 68, 289, 1156, 4913, 19652, 83521, 334084, 1419857, 5679428, 24137569, 96550276, 410338673, 1641354692, 6975757441, 27903029764, 118587876497, 474351505988, 2015993900449, 8063975601796, 34271896307633, 137087585230532, 582622237229761, 2330488948919044

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (0,17).

Formula

a(n) = 3*a(n-1) + 4*a(n-2) + 17^floor((n-2)/2).

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

a(n) = 17*a(n-2), n>1. - Harvey P. Dale, Jan 21 2012

E.g.f.: cosh(sqrt(17)*x) + 4*sinh(sqrt(17)*x)/sqrt(17). - Stefano Spezia, Mar 31 2023

Mathematica

CoefficientList[Series[(1+4x)/(1-17x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[ {0, 17}, {1, 4}, 30] (* Harvey P. Dale, Jan 21 2012 *)

Prog

(PARI) Vec((1+4*x)/(1-17*x^2) + O(x^40)) \\ Michel Marcus, Jan 26 2016
(Magma) I:=[1, 4, 17]; [n le 3 select I[n] else 17*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jan 26 2016

Crossrefs

Cf. A004663, A026383, A016116.

Sequence in context: A114587 A268431 A033114 * A363588 A344217 A033122

Adjacent sequences: A096878 A096879 A096880 * A096882 A096883 A096884

Keyword

easy,nonn

Author

Paul Barry, Jul 14 2004

Extensions

More terms from Stefano Spezia, Mar 31 2023

Status

approved