A136233 Matrix square of triangle U = A136228, read by rows.

1, 2, 1, 10, 8, 1, 75, 76, 14, 1, 753, 888, 196, 20, 1, 9534, 12542, 3087, 370, 26, 1, 146353, 209506, 55552, 7320, 598, 32, 1, 2647628, 4058806, 1136975, 159645, 14235, 880, 38, 1, 55251994, 89706276, 26224597, 3856065, 364403, 24480, 1216, 44, 1

Offset

0,2

Links

Table of n, a(n) for n=0..44.

Formula

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

Example

This triangle, U^2, begins:
1;
2, 1;
10, 8, 1;
75, 76, 14, 1;
753, 888, 196, 20, 1;
9534, 12542, 3087, 370, 26, 1;
146353, 209506, 55552, 7320, 598, 32, 1;
2647628, 4058806, 1136975, 159645, 14235, 880, 38, 1;
55251994, 89706276, 26224597, 3856065, 364403, 24480, 1216, 44, 1; ...
where column 0 of U^2 = column 1 of P = A136220.

Prog

(PARI) {T(n, k)=local(P=Mat(1), U=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]))))); (U^2)[n+1, k+1]}

Crossrefs

Cf. A136222 (column 0); related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W=P^3), A136236 (U^3).

Sequence in context: A213252 A122017 A219900 * A113088 A060694 A217108

Adjacent sequences: A136230 A136231 A136232 * A136234 A136235 A136236

Keyword

nonn,tabl

Author

Paul D. Hanna, Feb 07 2008

Status

approved