A172303 - OEIS

%I #2 Mar 30 2012 17:34:38

%S 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,

%T 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,

%U 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

%N 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.

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

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

%F 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)

%e 0;

%e 1;

%e 0,1;

%e 0,1,0,1;

%e 0,0,0,1,1,0,1;

%e 0,0,0,0,1,0,1,1,1,0,1;

%e 0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,1;

%t p[x,0]=0;

%t p[x,1]=1;

%t p[x_,n_]:=p[x,n]=x^(n-1)*p[x,n-1]+x^(n-1)*p[x,n-2];

%t Flatten[Table[CoefficientList[p[x,n],x],{n,0,10}]]

%K nonn,tabf

%O 0,56

%A _Roger L. Bagula_, Jan 31 2010

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