0,2

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

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; ...

(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]}

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

Adjacent sequences: A136229 A136230 A136231 this_sequence A136233 A136234 A136235

Sequence in context: A039812 A057869 A128417 this_sequence A079621 A046860 A089505

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Jan 28 2008