A113384 Triangle, read by rows, equal to the matrix square of A113381. Also given by: Q^2 = R*P = R*Q*(R^-2)*Q*R = P*Q*(P^-2)*Q*P, using triangular matrices P=A113370, Q=A113381 and R=A113389.

1, 4, 1, 22, 10, 1, 212, 130, 16, 1, 3255, 2365, 328, 22, 1, 70777, 57695, 8640, 616, 28, 1, 2022897, 1798275, 284356, 21197, 994, 34, 1, 72375484, 68931064, 11358500, 875424, 42196, 1462, 40, 1, 3130502129, 3155772612, 537277044, 42499204

Offset

0,2

Links

Table of n, a(n) for n=0..39.

Example

Triangle A113381^2 begins:
1;
4,1;
22,10,1;
212,130,16,1;
3255,2365,328,22,1;
70777,57695,8640,616,28,1;
2022897,1798275,284356,21197,994,34,1;
72375484,68931064,11358500,875424,42196,1462,40,1;
3130502129,3155772612,537277044,42499204,2094365,73797,2020,46,1;

Prog

(PARI) T(n, k)=local(A, B); A=Mat(1); for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3 || j==i || j>m-1, B[i, j]=1, if(j==1, B[i, 1]=1, B[i, j]=(A^(3*j-2))[i-j+1, 1])); )); A=B); (matrix(#A, #A, r, c, if(r>=c, (A^(3*c-1))[r-c+1, 1]))^2)[n+1, k+1]

Crossrefs

Cf. A113381, A113385 (column 0), A113386 (column 1); A113370, A113389.

Sequence in context: A360089 A299445 A135049 * A243663 A039812 A308559

Adjacent sequences: A113381 A113382 A113383 * A113385 A113386 A113387

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 14 2005

Status

approved