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A008927 Number of increasing sequences of star chain type with maximal element n. 1

%I #12 Oct 07 2013 11:31:21

%S 1,1,1,2,3,6,10,20,36,70,130,252,475,916,1745,3362,6438,12410,23852,

%T 46020,88697,171339,330938,640189,1238751,2399677,4650819,9021862,

%U 17510819,34013311,66106491,128568177,250191797,487168941,949133722

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

%C 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

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

%D M. Torelli, Increasing integer sequences and Goldbach's conjecture, preprint, 1996.

%D D. E. Knuth, The Art of Computer Programming; Addison-Wesley. Section 4.6.3.

%H M. Torelli, <a href="http://dx.doi.org/10.1051/ita:2006017">Increasing integer sequences and Goldbach's conjecture</a>, RAIRO - Theoretical Informatics and Applications, vol.40, no.02 (April 2006), pp.107-121.

%e a(5)=3 because 1,2,3,4,5; 1,2,3,5; 1,2,4,5 are star-kind addition chains.

%e a(8)=20 because there are 21 increasing addition chains up to 8, but 1,2,4,5,8 is not a star chain.

%Y Cf. A008928, A079301.

%K nonn

%O 1,4

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

%E More terms from _David W. Wilson_, Apr 01 2006

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Last modified June 6 16:18 EDT 2023. Contains 363148 sequences. (Running on oeis4.)