A102320 Triangular matrix, read by rows, that satisfies: T(n,k) = [T^2](n-1,k) when n>k>=0, with T(n,n) = (2*n+1).

1, 1, 3, 4, 9, 5, 33, 72, 25, 7, 436, 945, 300, 49, 9, 8122, 17568, 5425, 784, 81, 11, 197920, 427770, 130700, 18081, 1620, 121, 13, 6007205, 12979080, 3947050, 535864, 45441, 2904, 169, 15, 219413116, 473981445, 143812400, 19348042, 1599588, 95953

Offset

0,3

Comments

Column 0 forms A102321. Column 1 forms A102322. The contribution of each term along the main diagonal to column 0 is given by triangle of coefficients A102323.

Links

Table of n, a(n) for n=0..41.

Example

Rows of T begin:
[1],
[1,3],
[4,9,5],
[33,72,25,7],
[436,945,300,49,9],
[8122,17568,5425,784,81,11],
[197920,427770,130700,18081,1620,121,13],
[6007205,12979080,3947050,535864,45441,2904,169,15],...
Matrix square T^2 equals T excluding the main diagonal:
[1],
[4,9],
[33,72,25],
[436,945,300,49],
[8122,17568,5425,784,81],...

Prog

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

Crossrefs

Cf. A102086, A102321, A102322, A102323.

Sequence in context: A192334 A140439 A023183 * A227717 A021290 A016656

Adjacent sequences: A102317 A102318 A102319 * A102321 A102322 A102323

Keyword

nonn,tabl

Author

Paul D. Hanna, Jan 05 2005

Status

approved