A131270 Triangle T(n,k) = 2*A046854(n,k) - 1, read by rows.

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 5, 1, 1, 1, 5, 5, 7, 1, 1, 1, 5, 11, 7, 9, 1, 1, 1, 7, 11, 19, 9, 11, 1, 1, 1, 7, 19, 19, 29, 11, 13, 1, 1, 1, 9, 19, 39, 29, 41, 13, 15, 1, 1, 1, 9, 29, 39, 69, 41, 55, 15, 17, 1, 1, 1, 11, 29, 69, 69, 111, 55, 71, 17, 19, 1, 1

Offset: 0

Author

Gary W. Adamson, Jun 23 2007

Keywords

• nonn
• tabl

Comments

Row sums = A131269: {1, 2, 3, 6, 11, 20, 35, 60, 101, 168, ...}.

Examples

			First few rows of the triangle:
  1;
  1,  1;
  1,  1,  1;
  1,  3,  1,  1;
  1,  3,  5,  1,  1;
  1,  5,  5,  7,  1,  1;
  1,  5, 11,  7,  9,  1,  1;
  1,  7, 11, 19,  9, 11,  1,  1;
  ...
		

Links

• G. C. Greubel, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A046854, A065941, A000012, A131268, A131269.

Programs

Magma

[[2*Binomial(Floor((n+k)/2), k) -1: k in [0..n]]:n in [0..12]]; // G. C. Greubel, Jul 09 2019

Mathematica

Table[2*Binomial[Floor[(n+k)/2], k] - 1, {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Jul 09 2019 *)

PARI

T(n,k) = 2*binomial((n+k)\2, k)-1; \\ G. C. Greubel, Jul 09 2019

Sage

[[2*binomial(floor((n+k)/2), k) -1 for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jul 09 2019

Formula

T(n,k) = 2*A046854(n,k) - 1.

Reversed triangle of A131268.