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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
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
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
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