A114002 Expansion of g.f. x^k(1+x^(k+1))/(1-x^(k+1)).

1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 0, 0, 1, 2, 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Author

Paul Barry, Nov 12 2005

Keywords

• easy
• nonn
• tabl

Comments

Inverse is A114004. Row sums are A114003.

Examples

			Triangle begins:
  1;
  2, 1;
  2, 0, 1;
  2, 2, 0, 1;
  2, 0, 0, 0, 1;
  2, 2, 2, 0, 0, 1;
  2, 0, 0, 0, 0, 0, 1;
  ...
		

Crossrefs

Cf. A051731, A114003, A114004.

Programs

Mathematica

T[n_,k_]:=SeriesCoefficient[x^k(1+x^(k+1))/(1-x^(k+1)),{x,0,n}]; Table[T[n,k],{n,0,13},{k,0,n}] //Flatten (* Stefano Spezia, Sep 08 2023 *)

Formula

Column k has g.f. x^k(1+x^(k+1))/(1-x^(k+1)).

Equals 2*A051731 - I, I = Identity matrix. - Gary W. Adamson, Nov 07 2007