A134060 Triangle T(n,k) = A124927(n,k) + A134058(n,k) - A007318(n,k), read by rows.

1, 2, 3, 2, 6, 3, 2, 9, 9, 3, 2, 12, 18, 12, 3, 2, 15, 30, 30, 15, 3, 2, 18, 45, 60, 45, 18, 3, 2, 21, 63, 105, 105, 63, 21, 3, 2, 24, 84, 168, 210, 168, 84, 24, 3, 2, 27, 108, 252, 378, 378, 252, 108, 27, 3

Offset: 0

Author

Gary W. Adamson, Oct 05 2007

Keywords

• nonn
• tabl

Examples

			First few rows of the triangle are:
  1;
  2,  3;
  2,  6,  3;
  2,  9,  9,  3;
  2, 12, 18, 12,  3;
  2, 15, 30, 30, 15, 3;
  ...
		

Links

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

Crossrefs

Cf. A007318, A052940 (row sums), A127927, A134058.

Programs

Magma

[1] cat [k eq 0 select 2 else 3*Binomial(n,k): k in [0..n], n in [1..12]]; // G. C. Greubel, May 03 2021

Mathematica

Table[3*Binomial[n, k] -Boole[k==0] -Boole[n==0], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, May 03 2021 *)

Sage

def A134060(n,k): return 3*binomial(n,k) -bool(k==0) -bool(n==0)
flatten([[A134060(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 03 2021

Formula

T(n,k) = A124927(n,k) + A134058(n,k) - A007318(n,k) as infinite lower triangular matrices.

Sum_{k=0..n} T(n, k) = A052940(n).

T(n, k) = 3*binomial(n,k) - [k=0] - [n=0]. - G. C. Greubel, May 03 2021