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a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3).
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%I #36 Oct 10 2024 07:25:07

%S 1,6,23,100,421,1786,7563,32040,135721,574926,2435423,10316620,

%T 43701901,185124226,784198803,3321919440,14071876561,59609425686,

%U 252509579303,1069647742900,4531100550901,19194049946506,81307300336923,344423251294200,1459000305513721

%N a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,5,1).

%F a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3).

%F G.f.: -x*(1+3*x) / ( (1+x)*(x^2+4*x-1) ). a(n) + a(n+1) = A048876(n). - _R. J. Mathar_, Oct 22 2013

%F a(n) = (Lucas(3n-1) + (-1)^n)/2. - _Greg Dresden_, Oct 09 2020

%t LinearRecurrence[{3,5,1},{1,6,23},25] (* _James C. McMahon_, Oct 09 2024 *)

%Y Cf. A120758, A120757.

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_ and _Roger L. Bagula_, Jul 04 2006

%E Edited by _N. J. A. Sloane_, Dec 03 2006

%E a(24)-a(25) from _James C. McMahon_, Oct 09 2024