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A077029 Rectangle R(i,j) by antidiagonals; column j has j-1 zeros followed by numbers congruent to 1 mod j-1. 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 k-1, 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)=(i-j)(j-1)+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

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Last modified January 28 13:14 EST 2020. Contains 331321 sequences. (Running on oeis4.)