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

0,2

Comments

Inverse is A114004. Row sums are A114003.

Links

Table of n, a(n) for n=0..104.

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

Example

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;
  ...

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 *)

Crossrefs

Cf. A051731, A114003, A114004.

Sequence in context: A127442 A357524 A115628 * A114004 A306518 A333310

Adjacent sequences: A113999 A114000 A114001 * A114003 A114004 A114005

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 12 2005

Status

approved