A131301 Regular triangle read by rows: T(n,k) = 3*binomial(floor((n+k)/2),k)-2.

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

Offset: 0

Author

Gary W. Adamson, Jun 27 2007

Keywords

• nonn
• easy
• tabl

Comments

Row sums = A131300: (1, 2, 3, 7, 14, 27, 49, 86, ...). Reversed triangle = A131299.

Examples

			First few rows of the triangle:
  1;
  1,  1;
  1,  1,  1;
  1,  4,  1,  1;
  1,  4,  7,  1,  1;
  1,  7,  7, 10,  1,  1;
  1,  7, 16, 10, 13,  1,  1;
  ...
		

Links

• Nathaniel Johnston, Rows 0..100, flattened

Crossrefs

Cf. A046854, A000012, A131299, A131300.

Programs

Maple

for n from 0 to 6 do seq(3*binomial(floor((n+k)/2),k)-2,k=0..n); od; # Nathaniel Johnston, Jun 29 2011

Mathematica

t[n_, k_] := 3 Binomial[Floor[(n + k)/2], k] - 2; Table[t[n, k], {n, 11}, {k, 0, n}] // Flatten
(* to view triangle: Table[t[n, k], {n, 5}, {k, 0, n}] // TableForm *) (* Robert G. Wilson v, Feb 28 2015 *)

Formula

3*A046854 - 2*A000012 as infinite lower triangular matrices (former name).

T(n,k) = 3*binomial(floor((n+k)/2),k)-2. - Nathaniel Johnston, Jun 29 2011