A136237 - OEIS

%I #2 Mar 30 2012 18:37:08

%S 1,6,1,54,15,1,629,225,24,1,9003,3770,504,33,1,153276,71655,10988,891,

%T 42,1,3031553,1539315,259236,23903,1386,51,1,68406990,37072448,

%U 6688092,672672,44135,1989,60,1,1736020806,992226060,188767184,20225436,1442049

%N Matrix cube of triangle V = A136230, read by rows.

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

%e This triangle, V^3, begins:

%e 1;

%e 6, 1;

%e 54, 15, 1;

%e 629, 225, 24, 1;

%e 9003, 3770, 504, 33, 1;

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

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

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

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

%e where column 0 of V^3 = column 2 of P^2 = triangle A136225.

%o (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]}

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

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Feb 07 2008