A110023 A triangle of coefficients based on A000931 and Pascal's triangle: a(n)=a(n-2)+a(n-3); t(n,m)=a(n - m + 1)*a(m + 1)*Binomial[n, m].

1, 1, 1, 2, 2, 2, 2, 6, 6, 2, 3, 8, 24, 8, 3, 4, 15, 40, 40, 15, 4, 5, 24, 90, 80, 90, 24, 5, 7, 35, 168, 210, 210, 168, 35, 7, 9, 56, 280, 448, 630, 448, 280, 56, 9, 12, 81, 504, 840, 1512, 1512, 840, 504, 81, 12, 16, 120, 810, 1680, 3150, 4032, 3150, 1680, 810, 120, 16

Offset

1,4

Comments

Row sums are:

{1, 2, 6, 16, 46, 118, 318, 840, 2216, 5898, 15584}

Links

Table of n, a(n) for n=1..66.

Formula

a(n)=a(n-2)+a(n-3); t(n,m)=a(n - m + 1)*a(m + 1)*Binomial[n, m].

Example

{1},
{1, 1},
{2, 2, 2},
{2, 6, 6, 2},
{3, 8, 24, 8, 3},
{4, 15, 40, 40, 15, 4},
{5, 24, 90, 80, 90, 24, 5},
{7, 35, 168, 210, 210, 168, 35, 7},
{9, 56, 280, 448, 630, 448, 280, 56, 9},
{12, 81, 504, 840, 1512, 1512, 840, 504, 81, 12},
{16, 120, 810, 1680, 3150, 4032, 3150, 1680, 810, 120, 16}

Mathematica

Clear[t, a, n, m] a[0] = 1; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; t[n_, m_] := a[(n - m + 1)]*a[(m + 1)]*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}] Flatten[%]

Crossrefs

Cf. A141611, A141617, A000931.

Sequence in context: A075094 A238413 A151704 * A279466 A116863 A136494

Adjacent sequences: A110020 A110021 A110022 * A110024 A110025 A110026

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Aug 24 2008

Status

approved