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

0,9

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)

Links

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

Formula

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

Example

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;
  ...

Maple

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

Crossrefs

Cf. A065941, A000012, A131300, A131301.

Sequence in context: A321647 A323410 A182665 * A360911 A363977 A073937

Adjacent sequences: A131296 A131297 A131298 * A131300 A131301 A131302

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Jun 27 2007

Extensions

Better definition from Bruno Berselli, May 03 2012

Status

approved