A174988 Expansion of -x*(x-1)*(3*x+1) / (9*x^4-8*x^2+1).

0, 1, 2, 5, 16, 31, 110, 203, 736, 1345, 4898, 8933, 32560, 59359, 216398, 394475, 1438144, 2621569, 9557570, 17422277, 63517264, 115784095, 422119982, 769472267, 2805304480, 5113721281, 18643356002, 33984519845, 123899107696

Offset

0,3

Comments

Old name was: a(n)=2^Floor[n/2]*((1 + Sqrt[7])^n - (1 - Sqrt[7])^n)/(2^n*Sqrt[7]).

References

Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (0,8,0,-9).

Formula

a(n) = 8*a(n-2)-9*a(n-4). G.f.: -x*(x-1)*(3*x+1)/(9*x^4-8*x^2+1). [Colin Barker, Jan 05 2013]

Mathematica

f[n_] = 2^Floor[n/2]*((1 + Sqrt[7])^n - (1 - Sqrt[7])^n)/(2^n*Sqrt[7]);
Table[FullSimplify[ExpandAll[f[n]]], {n, 0, 30}]
LinearRecurrence[{0, 8, 0, -9}, {0, 1, 2, 5}, 30] (* Harvey P. Dale, Aug 21 2014 *)

Prog

(PARI) concat(0, Vec((1-x)*(3*x+1)/(9*x^4-8*x^2+1)+O(x^99))) \\ Charles R Greathouse IV, May 15 2013

Crossrefs

Sequence in context: A361257 A139022 A196025 * A364706 A053683 A305876

Adjacent sequences: A174985 A174986 A174987 * A174989 A174990 A174991

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 03 2010

Extensions

New name from Colin Barker, Jan 05 2013

Status

approved