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A345470 Number of self-complementary score sequences that are possible in an n-team round-robin tournament.

%I A345470 #56 Dec 23 2024 22:57:03
%S A345470 1,1,1,2,2,5,6,15,19,48,64,161,223,557,796,1971,2887,7090,10596,25826,
%T A345470 39256,95016,146533,352411,550328,1315827,2077418,4940587,7876036,
%U A345470 18639221,29971423,70608885,114422037,268436473,438068242
%N A345470 Number of self-complementary score sequences that are possible in an n-team round-robin tournament.
%C A345470 See A000571 for the definition of a score sequence.
%C A345470 A self-complementary score sequence W is a score sequence of win counts such that W = {s(1), s(2), ..., s(n)} and its complement, L={n-1-s(n), n-1-s(n-1), ..., n-1-s(1)}, a score sequence of loss counts, are identical.
%H A345470 Paul K. Stockmeyer, <a href="/A345470/b345470.txt">Table of n, a(n) for n = 0..500</a>
%H A345470 Paul K. Stockmeyer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Stockmeyer/stock14.html">Counting Various Classes of Tournament Score Sequences</a>, J. Integer Seq. 26 (2023), Article 23.5.2.
%e A345470 For n = 4 there are 4 score sequences of which only 2, those marked with an asterisk, are self-complementary.  These are the sequences for n=4.
%e A345470     {0,1,2,3} *
%e A345470     {0,2,2,2}
%e A345470     {1,1,1,3}
%e A345470     {1,1,2,2} *
%e A345470 For n = 5, there are 9 score sequences of which only 5, those marked with an asterisk, are self-complementary.  These are the sequences for n=5.
%e A345470     {0,1,2,3,4} *
%e A345470     {0,1,3,3,3}
%e A345470     {0,2,2,2,4} *
%e A345470     {0,2,2,3,3}
%e A345470     {1,1,2,3,3} *
%e A345470     {1,1,1,3,4}
%e A345470     {1,1,2,2,4}
%e A345470     {1,2,2,2,3} *
%e A345470     {2,2,2,2,2} *
%Y A345470 Cf. A000571.
%K A345470 nonn
%O A345470 0,4
%A A345470 _Howard Givner_, Jun 20 2021
%E A345470 a(30) corrected by _Howard Givner_, Jun 28 2021
%E A345470 a(0)=1 prepended and a(1) changed from 0 to 1 by _Howard Givner_, Feb 22 2022