A110102 A triangle of coefficients based on A000931: a(n) = a(n - 2) + a(n - 3); t(n,m) := a(n - m + 1)*a(m + 1).

1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 4, 2, 3, 4, 3, 4, 4, 3, 4, 5, 4, 6, 4, 6, 4, 5, 7, 5, 8, 6, 6, 8, 5, 7, 9, 7, 10, 8, 9, 8, 10, 7, 9, 12, 9, 14, 10, 12, 12, 10, 14, 9, 12, 16, 12, 18, 14, 15, 16, 15, 14, 18, 12, 16

Offset: 1

Author

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

Keywords

• nonn
• tabl

Comments

Row sums are:

{1, 2, 5, 8, 14, 22, 34, 52, 77, 114, 166}

Examples

			{1},
{1, 1},
{2, 1, 2},
{2, 2, 2, 2},
{3, 2, 4, 2, 3},
{4, 3, 4, 4, 3, 4},
{5, 4, 6, 4, 6, 4, 5},
{7, 5, 8, 6, 6, 8, 5, 7},
{9, 7, 10, 8, 9, 8, 10, 7, 9},
{12, 9, 14, 10, 12, 12, 10, 14, 9, 12},
{16, 12, 18, 14, 15, 16, 15, 14, 18, 12, 16}
		

Crossrefs

Cf. A141611, A141617, A000931.

Programs

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)]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Formula

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