A136234 Matrix square of triangle V = A136230, read by rows.

1, 4, 1, 26, 10, 1, 232, 110, 16, 1, 2657, 1435, 248, 22, 1, 37405, 22135, 4240, 440, 28, 1, 627435, 397820, 81708, 9295, 686, 34, 1, 12248365, 8203057, 1773156, 214478, 17248, 986, 40, 1, 273211787, 191405232, 43039532, 5442349, 463267, 28747, 1340

Offset

0,2

Links

Table of n, a(n) for n=0..42.

Formula

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

Example

This triangle, V^2, begins:
1;
4, 1;
26, 10, 1;
232, 110, 16, 1;
2657, 1435, 248, 22, 1;
37405, 22135, 4240, 440, 28, 1;
627435, 397820, 81708, 9295, 686, 34, 1;
12248365, 8203057, 1773156, 214478, 17248, 986, 40, 1;
273211787, 191405232, 43039532, 5442349, 463267, 28747, 1340, 46, 1; ...
where column 0 of V^2 = column 1 of P^2 = triangle A136225.

Prog

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

Crossrefs

Cf. A136227 (column 0); related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W=P^3), A136237 (V^3).

Sequence in context: A062328 A378199 A263918 * A196528 A135897 A039816

Adjacent sequences: A136231 A136232 A136233 * A136235 A136236 A136237

Keyword

nonn,tabl

Author

Paul D. Hanna, Feb 07 2008

Status

approved