A136236 Matrix cube of triangle U = A136228, read by rows.

1, 3, 1, 21, 12, 1, 208, 156, 21, 1, 2637, 2350, 399, 30, 1, 40731, 41034, 8029, 750, 39, 1, 742620, 821562, 177198, 18865, 1209, 48, 1, 15624420, 18631332, 4317936, 502335, 36478, 1776, 57, 1, 372892266, 473187270, 115949841, 14390880, 1136811

Offset

0,2

Links

Table of n, a(n) for n=0..40.

Formula

Column k of U^3 (this triangle) = column 2 of P^(3k+1), where P = triangle A136220.

Example

This triangle, U^3, begins:
1;
3, 1;
21, 12, 1;
208, 156, 21, 1;
2637, 2350, 399, 30, 1;
40731, 41034, 8029, 750, 39, 1;
742620, 821562, 177198, 18865, 1209, 48, 1;
15624420, 18631332, 4317936, 502335, 36478, 1776, 57, 1;
372892266, 473187270, 115949841, 14390880, 1136811, 62488, 2451, 66, 1;
where column 0 of U^3 = column 2 of P = A136220.

Prog

(PARI) {T(n, k)=local(P=Mat(1), U=Mat(1), PShR); if(n>0, for(i=0, n, PShR=matrix(#P, #P, r, c, if(r>=c, if(r==c, 1, if(c==1, 0, P[r-1, c-1])))); U=P*PShR^2; U=matrix(#P+1, #P+1, r, c, if(r>=c, if(r<#P+1, U[r, c], if(c==1, (P^3)[ #P, 1], (P^(3*c-1))[r-c+1, 1])))); P=matrix(#U, #U, r, c, if(r>=c, if(r<#R, P[r, c], (U^c)[r-c+1, 1]))))); (U^3)[n+1, k+1]}

Crossrefs

Cf. A136223 (column 0); related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W=P^3), A136233 (U^2).

Sequence in context: A143173 A000369 A225471 * A113090 A223549 A138354

Adjacent sequences: A136233 A136234 A136235 * A136237 A136238 A136239

Keyword

nonn,tabl

Author

Paul D. Hanna, Feb 07 2008

Status

approved