A136237 Matrix cube of triangle V = A136230, read by rows.

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

Offset: 0

Author

Paul D. Hanna, Feb 07 2008

Keywords

• nonn
• tabl

Examples

			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.
		

Crossrefs

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

Programs

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]}

Formula

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