A136232 Triangle, read by rows, equal to the matrix 4th power of triangle A136220.

1, 4, 1, 24, 8, 1, 198, 76, 12, 1, 2116, 888, 156, 16, 1, 28052, 12542, 2350, 264, 20, 1, 446560, 209506, 41034, 4864, 400, 24, 1, 8325700, 4058806, 821562, 100988, 8710, 564, 28, 1, 178284892, 89706276, 18631332, 2352116, 209440, 14168, 756, 32, 1

Offset: 0

Author

Paul D. Hanna, Jan 28 2008

Keywords

• nonn
• tabl

Examples

			This triangle P^4 begins:
1,
4, 1;
24, 8, 1;
198, 76, 12, 1;
2116, 888, 156, 16, 1;
28052, 12542, 2350, 264, 20, 1;
446560, 209506, 41034, 4864, 400, 24, 1;
8325700, 4058806, 821562, 100988, 8710, 564, 28, 1;
178284892, 89706276, 18631332, 2352116, 209440, 14168, 756, 32, 1; ...
where column k = column 1 of U^(k+1);
triangle U = A136228 begins:
1;
1, 1;
3, 4, 1;
15, 24, 7, 1;
108, 198, 63, 10, 1;
1036, 2116, 714, 120, 13, 1;
12569, 28052, 9884, 1725, 195, 16, 1; ...
where column k of U = column 0 of P^(3k+1) and
triangle P = A136220 begins:
1;
1, 1;
3, 2, 1;
15, 10, 3, 1;
108, 75, 21, 4, 1;
1036, 753, 208, 36, 5, 1;
12569, 9534, 2637, 442, 55, 6, 1; ...
		

Crossrefs

Cf. A136229 (column 0); related tables: A136220 (P), A136228 (U).

Programs

PARI

{T(n,k)=local(P=Mat(1),U,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])))));(P^4)[n+1,k+1]}

Formula

Column k of this triangle = column 1 of U^(k+1) where U = A136228.