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A345470 Number of self-complementary score sequences that are possible in an n-team round-robin tournament. 2
1, 1, 1, 2, 2, 5, 6, 15, 19, 48, 64, 161, 223, 557, 796, 1971, 2887, 7090, 10596, 25826, 39256, 95016, 146533, 352411, 550328, 1315827, 2077418, 4940587, 7876036, 18639221, 29971423, 70608885, 114422037, 268436473, 438068242 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
See A000571 for the definition of a score sequence.
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.
LINKS
Paul K. Stockmeyer, Counting Various Classes of Tournament Score Sequences, J. Integer Seq. 26 (2023), Article 23.5.2.
EXAMPLE
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.
{0,1,2,3} *
{0,2,2,2}
{1,1,1,3}
{1,1,2,2} *
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.
{0,1,2,3,4} *
{0,1,3,3,3}
{0,2,2,2,4} *
{0,2,2,3,3}
{1,1,2,3,3} *
{1,1,1,3,4}
{1,1,2,2,4}
{1,2,2,2,3} *
{2,2,2,2,2} *
CROSSREFS
Cf. A000571.
Sequence in context: A303931 A028410 A050216 * A368727 A320296 A329908
KEYWORD
nonn
AUTHOR
Howard Givner, Jun 20 2021
EXTENSIONS
a(30) corrected by Howard Givner, Jun 28 2021
a(0)=1 prepended and a(1) changed from 0 to 1 by Howard Givner, Feb 22 2022
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)