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%I #14 Mar 12 2024 12:16:39
%S 1,5,18,68,253,945,3526,13160,49113,183293,684058,2552940,9527701,
%T 35557865,132703758,495257168,1848324913,6898042485,25743845026,
%U 96077337620,358565505453,1338184684193,4994173231318,18638508241080
%N a(n) = 5a(n-1) - 5a(n-2) + a(n-3) + 2*(-1)^(n+1), alternatively a(n) = 3a(n-1) + 3a(n-2) - a(n-3).
%C See A109437 for comments.
%C Floretion Algebra Multiplication Program, FAMP Code: (-1)^(n)jbasejfor[ + .5'ii' + .5'kk' + .5'ij' + .5'ji' + .5'jk' + .5'kj'] 1vesfor = (-1,-1,-1,-1,)
%H Colin Barker, <a href="/A109438/b109438.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-1).
%F G.f.: (1+2*x) / ((x+1)*(x^2-4*x+1)).
%F a(n) = (-2*(-1)^n + (7-5*sqrt(3))*(2-sqrt(3))^n + (2+sqrt(3))^n*(7+5*sqrt(3))) / 12. - _Colin Barker_, May 12 2019
%t LinearRecurrence[{3,3,-1},{1,5,18},30] (* _Harvey P. Dale_, Sep 07 2021 *)
%o (PARI) Vec((1 + 2*x) / ((1 + x)*(1 - 4*x + x^2)) + O(x^30)) \\ _Colin Barker_, May 12 2019
%Y Cf. A109437, A001834, A102871.
%K easy,nonn
%O 0,2
%A _Creighton Dement_, Jun 28 2005
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