A134523 Triangle, read by rows, where column k of T = column 0 of matrix power T^{(k+1)(k+2)/2} for k>=0, with T(n,0)=1 for n>=0.

1, 1, 1, 1, 3, 1, 1, 12, 6, 1, 1, 75, 51, 10, 1, 1, 744, 636, 145, 15, 1, 1, 11181, 11406, 2980, 330, 21, 1, 1, 242835, 284541, 83890, 10095, 651, 28, 1, 1, 7330930, 9580386, 3133720, 411510, 27741, 1162, 36, 1, 1, 297801232, 424183235, 151359220

Offset

0,5

Links

Table of n, a(n) for n=0..48.

Example

Triangle T begins:
1;
1, 1;
1, 3, 1;
1, 12, 6, 1;
1, 75, 51, 10, 1;
1, 744, 636, 145, 15, 1;
1, 11181, 11406, 2980, 330, 21, 1;
1, 242835, 284541, 83890, 10095, 651, 28, 1;
1, 7330930, 9580386, 3133720, 411510, 27741, 1162, 36, 1; ...
Matrix cube, T^3, begins:
1;
3, 1;
12, 9, 1;
75, 90, 18, 1;
744, 1224, 333, 30, 1; ...
where column 0 of T^3 = column 1 of T.
Matrix 6th power, T^6, begins:
1;
6, 1;
51, 18, 1;
636, 342, 36, 1;
11406, 8145, 1206, 60, 1; ...
where column 0 of T^6 = column 2 of T.
1;
10, 1;
145, 30, 1;
2980, 930, 60, 1;
83890, 34635, 3210, 100, 1; ...
where column 0 of T^10 = column 3 of T.

Prog

(PARI) T(n, k)=local(A, B); A=matrix(1, 1); A[1, 1]=1; for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3 || j==i || j>m-1, B[i, j]=1, if(j==1, B[i, 1]=1, B[i, j]=(A^(j*(j+1)/2))[i-j+1, 1])); )); A=B); A[n+1, k+1]

Crossrefs

Cf. columns: A134524, A134525, A134526.

Sequence in context: A234944 A067402 A113340 * A098778 A078122 A128592

Adjacent sequences: A134520 A134521 A134522 * A134524 A134525 A134526

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 15 2007

Status

approved