

A102583


Triangular matrix, read by rows, where row n is formed from the first differences of row (n1) of its inverse matrix square, with an appended '1' for the main diagonal.


2



1, 1, 1, 2, 3, 1, 13, 19, 7, 1, 209, 310, 115, 15, 1, 7558, 11328, 4315, 575, 31, 1, 584837, 883178, 342761, 46965, 2607, 63, 1, 94047241, 142845383, 56217824, 7856782, 448173, 11199, 127, 1, 30883147262, 47124630966, 18750717425, 2660027115, 154716638, 3969645, 46655, 255, 1
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OFFSET

0,4


COMMENTS

Row sums are: {1,2,2,2,2,2,...}. Column 0 is A102585. Column 1 is A102586.


LINKS

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


FORMULA

T(n, k) = [T^2](n1, k)  [T^2](n1, k1) for n>k>0, with T(n, n)=1 for n>=0 and T(n, 0) = [T^2](n1, 0) for n>0.


EXAMPLE

Rows of matrix T begin:
[1],
[1,1],
[ 2,3,1],
[13,19,7,1],
[ 209,310,115,15,1],
[7558,11328,4315,575,31,1],
[ 584837,883178,342761,46965,2607,63,1],
[94047241,142845383,56217824,7856782,448173,11199,127,1],...
and is formed from the first differences of the rows
of the inverse matrix square, T^(2):
[1],
[ 2,1],
[13,6,1],
[ 209,101,14,1],
[7558,3770,545,30,1],
[ 584837,298341,44420,2545,62,1],...


PROG

(PARI) {T(n, k)=local(A=Mat(1), B); for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, if(j==1, B[i, j]=(A^2)[i1, 1], B[i, j]=(A^2)[i1, j](A^2)[i1, j1])); )); A=B); return(A[n+1, k+1])}


CROSSREFS

Cf. A102585, A102586, A102225.
Sequence in context: A107415 A079174 A204137 * A030780 A193683 A145643
Adjacent sequences: A102580 A102581 A102582 * A102584 A102585 A102586


KEYWORD

sign,tabl


AUTHOR

Paul D. Hanna, Jan 22 2005


STATUS

approved



