A135087 Triangle T(n, k) = 2*A134058(n, k) - 1, read by rows.

1, 3, 3, 3, 7, 3, 3, 11, 11, 3, 3, 15, 23, 15, 3, 3, 19, 39, 39, 19, 3, 3, 23, 59, 79, 59, 23, 3, 3, 27, 83, 139, 139, 83, 27, 3, 3, 31, 111, 223, 279, 223, 111, 31, 3, 3, 35, 143, 335, 503, 503, 335, 143, 35, 3

Offset: 0

Author

Gary W. Adamson, Nov 18 2007

Keywords

• nonn
• tabl

Examples

			First few rows of the triangle are:
  1;
  3,  3;
  3,  7,  3;
  3, 11, 11,  3;
  3, 15, 23, 15,  3;
  3, 19, 39, 39, 19,  3;
  3, 23, 59, 79, 59, 23, 3;
  ...
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A095768, A134058.

Programs

Magma

[1] cat [4*Binomial(n,k) -1: k in [0..n], n in [1..12]]; // G. C. Greubel, May 03 2021

Mathematica

Table[4*Binomial[n, k] -2*Boole[n==0] -1, {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, May 03 2021 *)

Sage

def A135087(n,k): return 4*binomial(n,k) -2*bool(n==0) -1
flatten([[A135087(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 03 2021

Formula

T(n, k) = 2*A134058(n, k) - 1.

From G. C. Greubel, May 03 2021: (Start)

T(n, k) = 4*binomial(n, k) - 2*[n=0] - 1.

Sum_{k=0..n} T(n, k) = 2^(n+2) - (n + 1 + 2*[n=0]) = A095768(n) - 2*[n=0]. (End)