A136235 Matrix square of triangle W = A136231; also equals P^6, where P = triangle A136220.

1, 6, 1, 48, 12, 1, 495, 150, 18, 1, 6338, 2160, 306, 24, 1, 97681, 36103, 5643, 516, 30, 1, 1767845, 694079, 115917, 11592, 780, 36, 1, 36839663, 15164785, 2657946, 282122, 20655, 1098, 42, 1, 870101407, 372225541, 67708113, 7502470, 580780

Offset

0,2

Links

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

Formula

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

Example

This triangle, W^2, begins:
1;
6, 1;
48, 12, 1;
495, 150, 18, 1;
6338, 2160, 306, 24, 1;
97681, 36103, 5643, 516, 30, 1;
1767845, 694079, 115917, 11592, 780, 36, 1;
36839663, 15164785, 2657946, 282122, 20655, 1098, 42, 1;
870101407, 372225541, 67708113, 7502470, 580780, 33480, 1470, 48, 1; ...
where column 0 of W^2 = column 1 of W = triangle A136231.

Prog

(PARI) {T(n, k)=local(P=Mat(1), U=Mat(1), W=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]))); W=P^3; )); (W^2)[n+1, k+1]}

Crossrefs

Cf. A136221 (column 0); related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W), A136238 (W^3).

Sequence in context: A049374 A283151 A138192 * A113392 A113387 A290316

Adjacent sequences: A136232 A136233 A136234 * A136236 A136237 A136238

Keyword

nonn,tabl

Author

Paul D. Hanna, Feb 07 2008

Status

approved