A132200 Numbers in (4,4)-Pascal triangle .

1, 4, 4, 4, 8, 4, 4, 12, 12, 4, 4, 16, 24, 16, 4, 4, 20, 40, 40, 20, 4, 4, 24, 60, 80, 60, 24, 4, 4, 28, 84, 140, 140, 84, 28, 4, 4, 32, 112, 224, 280, 224, 112, 32, 4, 4, 36, 144, 336, 504, 504, 336, 144, 36, 4, 4, 40, 180, 480, 840, 1008, 840, 480, 180, 40, 4

Offset: 0

Author

Philippe Deléham, Nov 19 2007

Keywords

• nonn
• tabl

Comments

This triangle belongs to the family of (x,y)-Pascal triangles ; other triangles arise by choosing different values for (x,y): (1,1) -> A007318 ; (1,0) -> A071919 ; (3,2) -> A029618 ; (2,2) -> A134058 ; (-1,1) -> A112467 ; (0,1) -> A097805 ; (5,5) -> A135089 ; etc..

Examples

			Triangle begins:
  1;
  4,  4;
  4,  8,  4;
  4, 12, 12,  4;
  4, 16, 24, 16,  4;
  4, 20, 40, 40, 20, 4;
		

Links

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

Crossrefs

Cf. A000079, A007318, A134058, A134059, A135089.

Programs

Magma

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

Mathematica

Table[4*Binomial[n,k] -3*Boole[n==0], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, May 03 2021 *)

Sage

def A132200(n,k): return 4*binomial(n,k) - 3*bool(n==0)
flatten([[A132200(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 03 2021

Formula

T(n,k) = 4*binomial(n,k), n>0 ; T(0,0)=1.

Sum_{k=0..n} T(n,k) = 2^(n+2) - 3*[n=0]. - G. C. Greubel, May 03 2021