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Search: id:A133139
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| A133139 |
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Number of generalised Ulam sequences including n as the third or higher term. |
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+0
1
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| 0, 0, 1, 2, 3, 5, 6, 10, 9, 12, 14, 17, 20, 20, 20, 29, 28, 31, 35, 35, 37, 40, 45, 51, 49, 55, 55, 58, 64, 61, 71, 76, 74, 76, 78, 87, 92, 91, 99, 97, 107, 100, 114, 107, 112, 119, 128, 132, 133, 127, 142, 140, 151, 146, 151, 154, 170, 158, 172, 164, 185, 179, 184, 186
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OFFSET
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1,4
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COMMENT
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I generalise the Ulam sequence by allowing any positive integer values (i and j) for the first two terms. Subsequent terms are all those integers which are a unique sum of two distinct earlier terms. In this sequence, a(n) is the number of distinct sequences (as defined by the first two terms) where 1 <= i < n-1 and i < j <= n-1.
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EXAMPLE
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a(10) = 12, since 10 occurs as a term in 12 different generalised Ulam sequences. The first two values of each are: (1,3) (1,4) (1,5) (1,6) (1,7) (1,8) (1,9) (2,6) (2,8) (3,4) (3,7) (4,6). It does not occur in the sequence (1,2) which runs: 1, 2, 3, 4, 6, 8, 11...
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CROSSREFS
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Cf. A002858.
Sequence in context: A051896 A061939 A029503 this_sequence A014593 A034044 A047447
Adjacent sequences: A133136 A133137 A133138 this_sequence A133140 A133141 A133142
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KEYWORD
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nonn
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AUTHOR
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Paul Richards (pr(AT)paulrichards.me.uk), Sep 21 2007
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