A136238 Matrix cube of triangle W = A136231; also equals P^9, where P = triangle A136220.

1, 9, 1, 99, 18, 1, 1323, 306, 27, 1, 21036, 5643, 621, 36, 1, 390012, 115917, 14580, 1044, 45, 1, 8287041, 2657946, 366129, 29754, 1575, 54, 1, 198918840, 67708113, 9968067, 882318, 52785, 2214, 63, 1, 5329794042, 1903562412, 294952140

Offset: 0

Author

Paul D. Hanna, Feb 07 2008

Keywords

• nonn
• tabl

Examples

			This triangle, W^3, begins:
1;
9, 1;
99, 18, 1;
1323, 306, 27, 1;
21036, 5643, 621, 36, 1;
390012, 115917, 14580, 1044, 45, 1;
8287041, 2657946, 366129, 29754, 1575, 54, 1;
198918840, 67708113, 9968067, 882318, 52785, 2214, 63, 1;
5329794042, 1903562412, 294952140, 27779046, 1804290, 85293, 2961, 72, 1;
where column 0 of W^3 = column 2 of W = triangle A136231.
		

Crossrefs

Cf. related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W), A136235 (W^2).

Programs

PARI

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

Formula

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