A131299 Triangle T(n,k) = 3*binomial(n-floor((k+1)/2), floor(k/2))-2 with k=0..n, read by rows.

1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 7, 4, 1, 1, 1, 10, 7, 7, 1, 1, 1, 13, 10, 16, 7, 1, 1, 1, 16, 13, 28, 16, 10, 1, 1, 1, 19, 16, 43, 28, 28, 10, 1, 1, 1, 22, 19, 61, 43, 58, 28, 13, 1, 1, 1, 25, 22, 82, 61, 103, 58, 43, 13, 1, 1, 1, 28, 25, 106, 82, 166

Offset: 0

Author

Gary W. Adamson, Jun 27 2007

Keywords

• nonn
• tabl
• easy

Comments

Row sums are in A131300. Reversed row triangle = A131301.

From R. J. Mathar, Apr 08 2013: (Start)

The matrix inverse starts

1;

-1, 1;

0, -1, 1;

0, 3, -4, 1;

0, -6, 9, -4, 1;

0, 30, -45, 21, -7, 1;

0, -132, 198, -93, 33, -7, 1;

0, 984, -1476, 693, -246, 54, -10, 1;

0, -6756, 10134, -4758, 1689, -372, 72, -10, 1;

0, 66972, -100458, 47166, -16743, 3687, -714, 102, -13, 1;

(End)

Examples

			Triangle begins:
  1;
  1,  1;
  1,  1,  1;
  1,  1,  4,  1;
  1,  1,  7,  4,  1;
  1,  1, 10,  7,  7,  1;
  1,  1, 13, 10, 16,  7,  1;
  ...
		

Links

• Nathaniel Johnston, Rows n = 0..100, flattened

Crossrefs

Cf. A065941, A000012, A131300, A131301.

Programs

Maple

A131299 := proc(n,k) 3*binomial(n-floor((k+1)/2),floor(k/2))-2 ; end proc; # Nathaniel Johnston, Jun 30 2011

Formula

3*A065941 - 2*A000012 as infinite lower triangular matrices.

Extensions

Better definition from Bruno Berselli, May 03 2012