A167601 G.f.: 1/(1-3*x-40*x^2-192*x^3).

1, 3, 49, 459, 3913, 39507, 363169, 3421083, 32375353, 303697827, 2862955537, 26952847467, 253686746665, 2388861601779, 22489001385601, 211729323587643, 1993409453728537, 18767289570726723, 176690276990149105

Offset: 0

Author

Roger L. Bagula, Nov 06 2009

Keywords

• nonn

Comments

The ratio limit a(n+1)/a(n) is 8*1.176845582834894... as n->infinity.

The constant is very close to A167288, so its signature sequence agrees with the signature sequence of A167288 to the 95th term.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (3, 40, 192).

Programs

Mathematica

Clear[p, q, x, t, n];
p[x_]:= -3 - 5 x - 3 x^2 + 8 *x^3;
q[x_]:= 1/Expand[x^3*p[1/x]];
a = Table[8^(n + 1)*SeriesCoefficient[ Series[q[t], {t, 0, 60}], n], {n, 0, 60}]
LinearRecurrence[{3,40,192},{1, 3, 49},100] (* G. C. Greubel, Jun 17 2016 *)

Formula

a(n) = 3*a(n-1) + 40*a(n-2) + 192*a(n-3). - G. C. Greubel, Jun 17 2016

Extensions

Definition simplified by the Associate Editors of the OEIS - Nov 12 2009.