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

0,4

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

Table of n, a(n) for n=0..29.

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

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 *)

Crossrefs

Cf. A372076.

Sequence in context: A179928 A026538 A358454 * A361932 A201951 A104448

Adjacent sequences: A372074 A372075 A372076 * A372078 A372079 A372080

Keyword

nonn

Author

N. J. A. Sloane, Jun 17 2024

Extensions

a(11) and beyond from Detlef Meya, Jun 22 2024

Status

approved