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

0,2

Links

Table of n, a(n) for n=0..38.

Formula

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

Example

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.

Prog

(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]}

Crossrefs

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

Sequence in context: A138342 A101678 A051380 * A113394 A243754 A254932

Adjacent sequences: A136235 A136236 A136237 * A136239 A136240 A136241

Keyword

nonn,tabl

Author

Paul D. Hanna, Feb 07 2008

Status

approved