0,2

Column 0 of this triangle = column 1 of square array A136217.

Let P=A136220, V=A136230, then column k of P^2 (this triangle) = column 0 of V^(k+1) while column j of V = column 0 of P^(3j+2).

Let P = A136220, then this triangle is P^2 and begins:

1;

2, 1;

8, 4, 1;

49, 26, 6, 1;

414, 232, 54, 8, 1;

4529, 2657, 629, 92, 10, 1;

61369, 37405, 9003, 1320, 140, 12, 1;

996815, 627435, 153276, 22606, 2385, 198, 14, 1;

18931547, 12248365, 3031553, 450066, 47500, 3904, 266, 16, 1; ...

where column k of P^2 = column 0 of V^(k+1) and

triangle V = A136230 begins:

1;

2, 1;

8, 5, 1;

49, 35, 8, 1;

414, 325, 80, 11, 1;

4529, 3820, 988, 143, 14, 1;

61369, 54800, 14696, 2200, 224, 17, 1; ...

where column k of V = column 0 of P^(3k+2).

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;

185704, 146353, 40731, 6742, 805, 78, 7, 1; ...

where column k of P = column 0 of U^(k+1) and U = A136228.

(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^2)[n+1, k+1]}

Cf. columns: A136226, A136227; related tables: A136228 (U), A136230 (V), A136231 (W=P^3), A136217, A136218.

Adjacent sequences: A136222 A136223 A136224 this_sequence A136226 A136227 A136228

Sequence in context: A109979 A110171 A104988 this_sequence A089460 A135520 A136230

nonn,tabl

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