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Search: id:A051336
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| A051336 |
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Number of arithmetic progressions in {1,2,3,...,n}, including trivial arithmetic progressions of lengths 1 and 2. |
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+0
4
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| 1, 3, 7, 13, 22, 33, 48, 65, 86, 110, 138, 168, 204, 242, 284, 330, 381, 434, 493, 554, 621, 692, 767, 844, 929, 1017, 1109, 1205, 1307, 1411, 1523, 1637, 1757, 1881, 2009, 2141, 2282, 2425, 2572, 2723, 2882, 3043, 3212, 3383, 3560, 3743, 3930, 4119
(list; graph; listen)
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OFFSET
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1,2
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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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Theorem: the second differences give tau(n+1), the number of divisors of n+1 (A000005).
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)). - Robert E. Sawyer (rs.1(AT)mindspring.com)
a(n) = n + sum { i=1..n-1, j=1..floor(n/i) } (n - i*j) - Robert E. Sawyer (rs.1(AT)mindspring.com)
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EXAMPLE
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a(1): [1]; a(2): [1],[2],[1,2]; a(3): [1],[2],[3],[1,2],[1,3],[2,3],[1,2,3]
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CROSSREFS
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a(n) = n + A078567(n).
Cf. A000005, A054519.
Sequence in context: A018367 A136219 A078582 this_sequence A002623 A081662 A091652
Adjacent sequences: A051333 A051334 A051335 this_sequence A051337 A051338 A051339
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KEYWORD
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nonn,easy,nice
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Nov 02 1999
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