A008927 Number of increasing sequences of star chain type with maximal element n.

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

Offset

1,4

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, Apr 01 2006

In other words, a(n) = the number of increasing star addition chains ending in n.

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.

Links

Table of n, a(n) for n=1..35.

M. Torelli, Increasing integer sequences and Goldbach's conjecture, RAIRO - Theoretical Informatics and Applications, vol.40, no.02 (April 2006), pp.107-121.

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.

Crossrefs

Cf. A008928, A079301.

Sequence in context: A173125 A047131 A231331 * A331488 A052525 A006606

Adjacent sequences: A008924 A008925 A008926 * A008928 A008929 A008930

Keyword

nonn

Author

Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it)

Extensions

More terms from David W. Wilson, Apr 01 2006

Status

approved