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A008927
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Number of increasing sequences of star chain type with maximal element n.
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1
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1, 1, 1, 2, 3, 6, 10, 20, 36, 70, 130, 252, 475, 916, 1745, 3362, 6438, 12410, 23852, 46020, 88697, 171339, 330938, 640189, 1238751, 2399677, 4650819, 9021862, 17510819, 34013311, 66106491, 128568177, 250191797, 487168941, 949133722
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(n) counts the Brauer addition chains for n, which are equivalent to star chains. In a Brauer chain, each element after the first is the sum of any previous element with the immediately previous element. This sequence counts all Brauer chains for n, not just the minimal ones, which are given by A079301. - David W. Wilson (davidwwilson(AT)comcast.net), Apr 01 2006
In other words, a(n) = the number of increasing star addition chains ending in n.
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REFERENCES
| M. Torelli, Increasing integer sequences and Goldbach's conjecture, preprint, 1996.
D. E. Knuth, The Art of Computer Programming; Addison-Wesley. Section 4.6.3.
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EXAMPLE
| a(5)=3 because 1,2,3,4,5; 1,2,3,5; 1,2,4,5 are star-kind addition chains.
a(8)=20 because there are 21 increasing addition chains up to 8, but 1,2,4,5,8 is not a star chain.
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CROSSREFS
| Cf. A008928, A079301.
Sequence in context: A036557 A173125 A047131 * A052525 A006606 A120421
Adjacent sequences: A008924 A008925 A008926 * A008928 A008929 A008930
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KEYWORD
| nonn
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AUTHOR
| torelli(AT)hermes.mc.dsi.unimi.it (Mauro Torelli)
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), Apr 01 2006
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