0,2

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

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.

(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]}

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

Adjacent sequences: A136231 A136232 A136233 this_sequence A136235 A136236 A136237

Sequence in context: A046860 A089505 A062328 this_sequence A135897 A039816 A118283

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Feb 07 2008