

A077029


Rectangle R(i,j) by antidiagonals; column j has j1 zeros followed by numbers congruent to 1 mod j1.


1



1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 1, 0, 0, 1, 4, 3, 0, 0, 0, 1, 5, 5, 1, 0, 0, 0, 1, 6, 7, 4, 0, 0, 0, 0, 1, 7, 9, 7, 1, 0, 0, 0, 0, 1, 8, 11, 10, 5, 0, 0, 0, 0, 0, 1, 9, 13, 13, 9, 1, 0, 0, 0, 0, 0, 1, 10, 15, 16, 13, 6, 0, 0, 0, 0, 0, 0, 1, 11, 17, 19, 17, 11, 1, 0, 0, 0, 0, 0, 0, 1, 12, 19, 22
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,8


COMMENTS

The number of occurrences of k is the number of divisors of k1, for k>=2. Column 1 of the inverse of this infinite matrix begins with (1,1,1,1,2,6,24,120,6!,7!,8!,9!,...). The remaining columns are likewise expressible in terms of factorials.


LINKS

Table of n, a(n) for n=1..95.


FORMULA

R(i, j)=(ij)(j1)+1 if 1<=i<=j; R(i, j)=0 if j>=i+1.


EXAMPLE

Northwest corner:
1 0 0 0 0 0
1 1 0 0 0 0
1 2 1 0 0 0
1 3 3 1 0 0
1 4 5 4 1 0
1 5 7 7 5 1


CROSSREFS

Cf. A077028.
Sequence in context: A216599 A114510 A325466 * A052553 A290054 A290430
Adjacent sequences: A077026 A077027 A077028 * A077030 A077031 A077032


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Oct 19 2002


STATUS

approved



