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Search: id:A078567
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| A078567 |
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Number of arithmetic subsequences of [1,...,n] with length > 1. |
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+0
4
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| 0, 1, 4, 9, 17, 27, 41, 57, 77, 100, 127, 156, 191, 228, 269, 314, 364, 416, 474, 534, 600, 670, 744, 820, 904, 991, 1082, 1177, 1278, 1381, 1492, 1605, 1724, 1847, 1974, 2105, 2245, 2387, 2533, 2683, 2841, 3001, 3169, 3339, 3515, 3697, 3883
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The number of arithmetic subsequences of [1,...,n] with successive-term increment i and length k is (n-i*(k-1))(i > 0, k > 0, n > i*(k-1)).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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a(n) = sum { i=1..n-1, j=1..floor((n-1)/i) } (n - i*j)
Convolution of A000027 and A000005. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 08 2006
Row sums of triangle A134546 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 31 2007
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EXAMPLE
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a(2): [1,2]; a(3): [1,2],[1,3],[2,3],[1,2,3]
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CROSSREFS
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Cf. A051336, A134546.
Appears to be the partial sums of A006218. - N. J. A. Sloane (njas(AT)research.att.com), Nov 24 2008
Sequence in context: A033607 A019572 A048205 this_sequence A033617 A033613 A033608
Adjacent sequences: A078564 A078565 A078566 this_sequence A078568 A078569 A078570
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KEYWORD
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nonn,easy
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AUTHOR
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Robert E. Sawyer (rs.1(AT)mindspring.com)
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