|
|
A109284
|
|
Column 1 of triangle A109282.
|
|
4
|
|
|
1, 2, 6, 36, 258, 2190, 20988, 222042, 2554890, 31606740, 416907618, 5824488540, 85725372240, 1323363947268, 21348018188394, 358735098433608, 6262471636627866, 113303272081250532, 2120102973225741564
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Triangular matrix T=A109282 satisfies: T(n,k) = [T^3](n-1,k) for n>k+1>=1, with T(n,n) = 1 and T(n+1,n) = n+1 for n>=0; also, T^(m+3) = SHIFT_UP(T^(m+1) - T^m) - D*T^m for all m where diagonal matrix D = [0,1,2,3,...] and SHIFT_UP shifts each column up 1 row.
|
|
LINKS
|
|
|
PROG
|
(PARI) {a(n)=local(M=matrix(n+2, n+2)); M=M^0; for(i=1, n, M=matrix(n+2, n+2, r, c, if(r>=c, if(r==c, 1, if(r==c+1, c, (M^3)[r-1, c]))))); return(M[n+2, 2])}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|