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 A372077 #24 Apr 11 2025 03:26:04
%S A372077 0,0,1,3,6,13,33,84,205,495,1206,2953,7221,17628,43033,105099,256710,
%T A372077 626965,1531161,3739428,9132661,22304343,54472758,133035889,324906765,
%U A372077 793503660,1937934241,4732918803,11558968326,28229885533
%N A372077 The sequence T_{3,2}(n,3).
%D A372077 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 A372077 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,4).
%F A372077 a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-2} Sum_{k=0..n-i-j-2} binomial(n - i - j - 2, 3*k)*3^k. a(n+1) = a(n) + A372076(n). - _Detlef Meya_, Jun 22 2024
%F A372077 G.f.: x^2/(1-3*x+3*x^2-4*x^3). - _Georg Fischer_, Apr 10 2025, from the reference, p. 108.
%t A372077 a[n_] := Sum[Sum[Sum[Binomial[n - i - j - 2, 3*k]*3^k, {k,0,n-i-j-2}], {j,0,n-i-2}], {i,0,n-1}]; Table[a[n], {n,0,29}] (* _Detlef Meya_, Jun 22 2024 *)
%Y A372077 Cf. A372076.
%K A372077 nonn,easy
%O A372077 0,4
%A A372077 _N. J. A. Sloane_, Jun 17 2024
%E A372077 a(11) and beyond from _Detlef Meya_, Jun 22 2024