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Search: id:A143786
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| A143786 |
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Number of arithmetic progressions from m to n; a rectangular array, m>=0, n>=0, by antidiagonals. |
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+0
1
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| 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 3, 2, 1, 2, 3, 2, 2, 1, 1, 2, 2, 4, 3, 2, 1, 2, 3, 4, 2, 2, 2, 1, 1, 2, 2, 2, 4, 4, 3, 2, 1, 2, 3, 4, 4, 3, 2, 2, 2, 1, 1, 2, 2, 2, 3, 4, 4, 4, 3, 2, 1, 2, 3, 4, 4, 4, 2, 3, 2, 2, 2, 1, 1, 2, 2, 2, 3, 2, 6, 4, 4, 4, 3, 2, 1, 2, 3, 4, 4, 4, 6, 2, 2, 3, 2, 2, 2, 1, 1, 2, 2, 2, 3, 2, 2
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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T(m,n) = number of solutions (h,k) of n=m+hk, where h>=0, k>=0. Except for initial terms every row (and column) is A000005.
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EXAMPLE
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Northwest corner:
1 1 2 2 3 2 4
1 1 1 2 2 3 2
2 1 1 1 2 2 3
2 2 1 1 1 2 2
3 2 2 1 1 1 2
T(8,2) counts these 4 arithmetic progressions:
2,3,4,5,6,7,8; 2,4,6,8; 2,5,8; and 2,8.
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CROSSREFS
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Cf. A000005.
Sequence in context: A161175 A095955 A078573 this_sequence A035176 A011793 A109649
Adjacent sequences: A143783 A143784 A143785 this_sequence A143787 A143788 A143789
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Sep 01 2008
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