This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372076 #24 Apr 11 2025 03:34:12
%S A372076 0,1,2,3,7,20,51,121,290,711,1747,4268,10407,25405,62066,151611,
%T A372076 370255,904196,2208267,5393233,13171682,32168415,78563131,191870876,
%U A372076 468596895,1144430581,2794984562,6826049523,16670917207,40714541300
%N A372076 The sequence T_{3,1}(n,3).
%D A372076 Maribel Díaz Noguera [Maribel Del Carmen Díaz Noguera], Rigoberto Flores, Jose L. Ramirez, and Martha Romero Rojas, Catalan identities for generalized Fibonacci polynomials, Fib. Q., 62:2 (2024), 100-111. See Table 3.
%H A372076 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,4).
%F A372076 a(n) = Sum_{j=0..n-1} Sum_{k=0..n-j-1} binomial(n - j - 1, 3*k)*3^k. a(n+1) = a(n) + A097122(n). - _Detlef Meya_, Jun 22 2024
%F A372076 G.f.: (x-x^2)/(1-3*x+3*x^2-4*x^3). - _Georg Fischer_, Apr 10 2025, from the reference, p. 108.
%t A372076 a[n_] := Sum[Sum[Binomial[n - j - 1, 3*k]*3^k, {k,0,n-j-1}], {j,0,n-1}]; Table[a[n], {n,0,29}] (* _Detlef Meya_, Jun 22 2024 *)
%Y A372076 Cf. A097122, A372077.
%K A372076 nonn,easy
%O A372076 0,3
%A A372076 _N. J. A. Sloane_, Jun 17 2024
%E A372076 a(11) and beyond from _Detlef Meya_, Jun 22 2024