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A098183 a(n) = 3*a(n-1) + a(n-3), a(0) = 1, a(1) = 1, a(2) = 4.

%I A098183 #15 May 25 2022 19:19:42
%S A098183 1,1,4,13,40,124,385,1195,3709,11512,35731,110902,344218,1068385,
%T A098183 3316057,10292389,31945552,99152713,307750528,955197136,2964744121,
%U A098183 9201982891,28561145809,88648181548,275146527535,854000728414,2650650366790,8227097627905,25535293612129
%N A098183 a(n) = 3*a(n-1) + a(n-3), a(0) = 1, a(1) = 1, a(2) = 4.
%H A098183 Alois P. Heinz, <a href="/A098183/b098183.txt">Table of n, a(n) for n = 0..1000</a>
%H A098183 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,1).
%F A098183 G.f.: (1-x)^2/(1-3*x-x^3).
%F A098183 a(n) = Sum_{k=0..floor(n/2)} binomial(n+k,3*k) * 3^k.
%p A098183 a:= proc(n) option remember;
%p A098183       `if`(n<2, 1, 3*a(n-1)+a(n-3))
%p A098183     end:
%p A098183 seq(a(n), n=0..30);  # _Alois P. Heinz_, May 25 2022
%Y A098183 Cf. A098182, A098184.
%K A098183 nonn,easy
%O A098183 0,3
%A A098183 _Paul Barry_, Aug 30 2004