|
| |
|
|
A185624
|
|
Triangle, read by rows, equal to the matrix square of triangle A185620.
|
|
6
|
|
|
|
1, 2, 1, 3, 2, 1, 6, 7, 2, 1, 18, 28, 11, 2, 1, 79, 142, 66, 15, 2, 1, 463, 913, 470, 120, 19, 2, 1, 3396, 7244, 3997, 1098, 190, 23, 2, 1, 30073, 69004, 40079, 11587, 2122, 276, 27, 2, 1, 314037, 771359, 466448, 140092, 26707, 3638, 378, 31, 2, 1, 3796561, 9933242, 6208551, 1921122
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Table of n, a(n) for n=0..58.
|
|
|
EXAMPLE
|
Triangle begins:
1;
2, 1;
3, 2, 1;
6, 7, 2, 1;
18, 28, 11, 2, 1;
79, 142, 66, 15, 2, 1;
463, 913, 470, 120, 19, 2, 1;
3396, 7244, 3997, 1098, 190, 23, 2, 1;
30073, 69004, 40079, 11587, 2122, 276, 27, 2, 1;
314037, 771359, 466448, 140092, 26707, 3638, 378, 31, 2, 1;
3796561, 9933242, 6208551, 1921122, 377495, 53149, 5742, 496, 35, 2, 1; ...
This triangle equals the matrix square, R^2, of triangle R = A185620, which begins:
1;
1, 1;
1, 1, 1;
1, 3, 1, 1;
1, 10, 5, 1, 1;
1, 42, 27, 7, 1, 1;
1, 226, 173, 52, 9, 1, 1;
1, 1525, 1330, 442, 85, 11, 1, 1;
1, 12555, 12134, 4345, 897, 126, 13, 1, 1; ...
where R^3 - R^2 + I equals R shifted left one column.
|
|
|
PROG
|
(PARI) {T(n, k)=local(A=Mat(1), B); for(m=1, n, B=A^3-A^2+A^0; A=matrix(m+1, m+1); for(i=1, m+1, for(j=1, i, if(i<2|j==i, A[i, j]=1, if(j==1, A[i, j]=1, A[i, j]=B[i-1, j-1]))))); return((A^2)[n+1, k+1])}
|
|
|
CROSSREFS
|
Cf. A185620, A185625, A185626, A185627, A185628.
Sequence in context: A054098 A132089 A321155 * A162387 A107880 A102228
Adjacent sequences: A185621 A185622 A185623 * A185625 A185626 A185627
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Paul D. Hanna, Sep 07 2011
|
|
|
STATUS
|
approved
|
| |
|
|
