A142597 Triangle read by rows: t(n,k)=t(n - 1, k - 1) + 4* t(n - 1, k) + 3*t(n - 1, k - 1).

1, 1, 1, 1, 8, 1, 1, 36, 36, 1, 1, 148, 288, 148, 1, 1, 596, 1744, 1744, 596, 1, 1, 2388, 9360, 13952, 9360, 2388, 1, 1, 9556, 46992, 93248, 93248, 46992, 9556, 1, 1, 38228, 226192, 560960, 745984, 560960, 226192, 38228, 1, 1, 152916, 1057680, 3148608

Offset: 1

Author

Roger L. Bagula, Sep 22 2008

Keywords

• nonn
• tabl

Comments

Row sums are: {1, 2, 10, 74, 586, 4682, 37450, 299594, 2396746, 19173962, ...}.

Examples

			Triangle begins:
{1},
{1, 1},
{1, 8, 1},
{1, 36, 36, 1},
{1, 148, 288, 148, 1},
{1, 596, 1744, 1744, 596, 1},
{1, 2388, 9360, 13952, 9360, 2388, 1},
{1, 9556, 46992, 93248, 93248, 46992, 9556, 1},
{1, 38228, 226192, 560960, 745984, 560960, 226192, 38228, 1},
{1, 152916, 1057680, 3148608, 5227776, 5227776, 3148608, 1057680, 152916, 1}
		

Crossrefs

Cf. A142175, A142467.

Cf. A008292, A119258, A060187, A142175, A142467.

Programs

Mathematica

A[n_, 1] := 1 A[n_, n_] := 1 A[n_, k_] := A[n - 1, k - 1] + 4* A[n - 1, k] + 3*A[n - 1, k - 1]; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]

Extensions

Edited by N. J. A. Sloane, Dec 07 2008