A167601 - OEIS

%I #7 Jun 18 2016 00:43:38

%S 1,3,49,459,3913,39507,363169,3421083,32375353,303697827,2862955537,

%T 26952847467,253686746665,2388861601779,22489001385601,

%U 211729323587643,1993409453728537,18767289570726723,176690276990149105

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

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

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

%H G. C. Greubel, <a href="/A167601/b167601.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, 40, 192).

%F a(n) = 3*a(n-1) + 40*a(n-2) + 192*a(n-3). - _G. C. Greubel_, Jun 17 2016

%t Clear[p, q, x, t, n];

%t p[x_]:= -3 - 5 x - 3 x^2 + 8 *x^3;

%t q[x_]:= 1/Expand[x^3*p[1/x]];

%t a = Table[8^(n + 1)*SeriesCoefficient[ Series[q[t], {t, 0, 60}], n], {n, 0, 60}]

%t LinearRecurrence[{3,40,192},{1, 3, 49},100] (* _G. C. Greubel_, Jun 17 2016 *)

%K nonn

%O 0,2

%A _Roger L. Bagula_, Nov 06 2009

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