A372077 The sequence T_{3,2}(n,3).
0, 0, 1, 3, 6, 13, 33, 84, 205, 495, 1206, 2953, 7221, 17628, 43033, 105099, 256710, 626965, 1531161, 3739428, 9132661, 22304343, 54472758, 133035889, 324906765, 793503660, 1937934241, 4732918803, 11558968326, 28229885533
Offset: 0
References
- 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.
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,4).
Crossrefs
Cf. A372076.
Programs
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Mathematica
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 *)
Formula
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
G.f.: x^2/(1-3*x+3*x^2-4*x^3). - Georg Fischer, Apr 10 2025, from the reference, p. 108.
Extensions
a(11) and beyond from Detlef Meya, Jun 22 2024