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A077029
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Rectangle R(i,j) by antidiagonals; column j has j-1 zeros followed by numbers congruent to 1 mod j-1.
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1
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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; internal format)
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OFFSET
| 1,8
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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.
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FORMULA
| R(i, j)=(i-j)(j-1)+1 if 1<=i<=j; R(i, j)=0 if j>=i+1.
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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
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CROSSREFS
| Cf. A077028.
Sequence in context: A029373 A029362 A114510 * A052553 A045847 A137586
Adjacent sequences: A077026 A077027 A077028 * A077030 A077031 A077032
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Oct 19 2002
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