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

0,2

Links

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

Formula

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

Example

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; ...

Prog

(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]}

Crossrefs

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

Sequence in context: A128417 A257532 A183875 * A079621 A285061 A285066

Adjacent sequences: A136229 A136230 A136231 * A136233 A136234 A136235

Keyword

nonn,tabl

Author

Paul D. Hanna, Jan 28 2008

Status

approved