A104446 Square of triangular matrix A104445, read by rows, where X=A104445 satisfies: SHIFT_LEFT_UP(X) = X^2 - X + I.

1, 2, 1, 3, 2, 1, 5, 5, 2, 1, 10, 13, 7, 2, 1, 25, 39, 25, 9, 2, 1, 78, 139, 100, 41, 11, 2, 1, 296, 587, 459, 205, 61, 13, 2, 1, 1330, 2897, 2418, 1149, 366, 85, 15, 2, 1, 6935, 16462, 14506, 7233, 2421, 595, 113, 17, 2, 1, 41352, 106301, 98161, 50905, 17706, 4535, 904

Offset

0,2

Comments

Column 0: T(n,0) = 1 + A091352(n-1) for n>0. Column 1 is A104447. Row sums form A104448.

Links

Table of n, a(n) for n=0..61.

Formula

T(n, k) = A104445(n, k) + A104445(n+1, k+1) - I(n, k), where I=identity matrix. T(n, k) = A091351(n-1, k) + A091351(n, k+1) - I(n, k), for n>k>=0.

Example

Rows begin:
1;
2,1;
3,2,1;
5,5,2,1;
10,13,7,2,1;
25,39,25,9,2,1;
78,139,100,41,11,2,1;
296,587,459,205,61,13,2,1;
1330,2897,2418,1149,366,85,15,2,1
6935,16462,14506,7233,2421,595,113,17,2,1; ...

Prog

(PARI) T(n, k)=local(A=Mat(1), B); for(m=1, n, B=A^2-A+A^0; A=matrix(m+1, m+1); for(i=1, m+1, for(j=1, i, if(i<2 || j==i, A[i, j]=1, if(j==1, A[i, j]=1, A[i, j]=B[i-1, j-1]))))); return((A^2)[n+1, k+1])

Crossrefs

Cf. A104445, A091351, A091352, A104447, A104448.

Sequence in context: A091355 A131245 A179927 * A131345 A134423 A061260

Adjacent sequences: A104443 A104444 A104445 * A104447 A104448 A104449

Keyword

nonn,tabl

Author

Paul D. Hanna, Mar 08 2005

Status

approved