0,2

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

This triangle, V^3, begins:

1;

6, 1;

54, 15, 1;

629, 225, 24, 1;

9003, 3770, 504, 33, 1;

153276, 71655, 10988, 891, 42, 1;

3031553, 1539315, 259236, 23903, 1386, 51, 1;

68406990, 37072448, 6688092, 672672, 44135, 1989, 60, 1;

1736020806, 992226060, 188767184, 20225436, 1442049, 73304, 2700, 69, 1;

where column 0 of V^3 = column 2 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^3)[n+1, k+1]}

Cf. related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W=P^3), A136234 (V^2).

Sequence in context: A113392 A113387 A090435 this_sequence A083837 A049213 A165886

Adjacent sequences: A136234 A136235 A136236 this_sequence A136238 A136239 A136240

nonn,tabl

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