A141715 Matrix square of triangle T = A141712, where the n-th diagonal of T equals the BINOMIAL transform of the (n-1)-th diagonal of T^2.

1, 2, 1, 6, 4, 1, 26, 20, 8, 1, 162, 136, 68, 16, 1, 1454, 1292, 732, 236, 32, 1, 18854, 17400, 10648, 4036, 836, 64, 1, 354258, 335404, 215708, 90152, 22692, 3020, 128, 1, 9671546, 9317288, 6192440, 2752332, 780400, 129556, 11108, 256, 1, 384587782

Offset

0,2

Links

Table of n, a(n) for n=0..45.

Example

This triangle, T^2, begins:
1;
2, 1;
6, 4, 1;
26, 20, 8, 1;
162, 136, 68, 16, 1;
1454, 1292, 732, 236, 32, 1;
18854, 17400, 10648, 4036, 836, 64, 1;
354258, 335404, 215708, 90152, 22692, 3020, 128, 1;
9671546, 9317288, 6192440, 2752332, 780400, 129556, 11108, 256, 1; ...
Triangle T=A141712 begins:
1;
1, 1;
2, 2, 1;
6, 6, 4, 1;
26, 26, 18, 8, 1;
162, 162, 114, 54, 16, 1;
1454, 1454, 1030, 506, 162, 32, 1;
18854, 18854, 13394, 6666, 2274, 486, 64, 1; ...
where the BINOMIAL transform of diagonal 2 of T^2:
BINOMIAL[6,20,68,236,836,3020,11108,41516,...]
equals: [6,26,114,506,2274,10346,47634,221786,...]
which is diagonal 3 of T.

Prog

(PARI) {T(n, k)=local(M, M2); if(n==k, 1, if(n==k+1, 2^n, M=matrix(n+1, n+1, r, c, if(r==c, 1, if(r>=c, sum(j=0, c-1, binomial(c-1, j)*T(r-c+j-1, j)) ))); (M^2)[n+1, k+1]))}

Crossrefs

Cf. A141712 (T), A141713 (column 0), A141716 (column 1).

Sequence in context: A112356 A135885 A162312 * A329431 A328923 A263271

Adjacent sequences: A141712 A141713 A141714 * A141716 A141717 A141718

Keyword

nonn,tabl

Author

Paul D. Hanna, Jul 01 2008

Status

approved