This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A008927 #20 Apr 30 2025 09:11:09 %S A008927 1,1,1,2,3,6,10,20,36,70,130,252,475,916,1745,3362,6438,12410,23852, %T A008927 46020,88697,171339,330938,640189,1238751,2399677,4650819,9021862, %U A008927 17510819,34013311,66106491,128568177,250191797,487168941,949133722,1850211247,3608650388 %N A008927 Number of increasing sequences of star chain type with maximal element n. %C A008927 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 A008927 In other words, a(n) = the number of increasing star addition chains ending in n. %D A008927 M. Torelli, Increasing integer sequences and Goldbach's conjecture, preprint, 1996. %D A008927 D. E. Knuth, The Art of Computer Programming; Addison-Wesley. Section 4.6.3. %H A008927 Martin Fuller, <a href="/A008927/b008927.txt">Table of n, a(n) for n = 1..70</a> %H A008927 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. %F A008927 Conjecture: a(n) ~ 2^n/n. - _Martin Fuller_, Apr 29 2025 %e A008927 a(5)=3 because 1,2,3,4,5; 1,2,3,5; 1,2,4,5 are star-kind addition chains. %e A008927 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 A008927 Cf. A008928, A079301. %K A008927 nonn %O A008927 1,4 %A A008927 Mauro Torelli (torelli(AT)hermes.mc.dsi.unimi.it) %E A008927 More terms from _David W. Wilson_, Apr 01 2006