A172303 Table T(n,k) with coefficients [x^k] of the polynomials p(x,n) = x^(n-1)*p(x,n-1) + x^(n-2)*p(x,n-2), recurrence starting p(x,0)=0, p(x,1)=1.

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

Offset

0,56

Comments

Row sums are sum_{k>=0} T(n,k) = A000045(n).

Lengths of the rows (1 + the degrees of the polynomials) are: 0, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46,..., A000124

Links

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

Formula

T(n,k)= [x^k] p(x,n). p(x,n)=x^(n - 1)*p(x, n - 1) + x^(n - 2)*p(x, n - 2)

Example

0;
1;
0,1;
0,1,0,1;
0,0,0,1,1,0,1;
0,0,0,0,1,0,1,1,1,0,1;
0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,1;

Mathematica

p[x, 0]=0;
p[x, 1]=1;
p[x_, n_]:=p[x, n]=x^(n-1)*p[x, n-1]+x^(n-1)*p[x, n-2];
Flatten[Table[CoefficientList[p[x, n], x], {n, 0, 10}]]

Crossrefs

Sequence in context: A108149 A128583 A218854 * A064391 A236470 A206589

Adjacent sequences: A172300 A172301 A172302 * A172304 A172305 A172306

Keyword

nonn,tabf

Author

Roger L. Bagula, Jan 31 2010

Extensions

Keyword tabf added; A-sequences of row sums and lengths identified. The Assoc. Editors of the OEIS - Feb 02 2010

Status

approved