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Search: id:A002137
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| A002137 |
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Number of n X n symmetric matrices with positive entries, trace 0 and all row sums 2.
(Formerly M4154 N1726)
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+0
3
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| 1, 0, 1, 1, 6, 22, 130, 822, 6202, 52552, 499194, 5238370, 60222844, 752587764, 10157945044, 147267180508, 2282355168060, 37655004171808, 658906772228668, 12188911634495388, 237669544014377896, 4871976826254018760, 104742902332392298296
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. C. Aitken, On the number of distinct terms in the expansion of symmetric and skew determinants, Edinburgh Math. Notes, No. 34 (1944), 1-5.
I. M. H. Etherington, Some problems of non-associative combinations, Edinburgh Math. Notes, 32 (1940), 1-6.
P. A. MacMahon, Combinations derived from m identical sets of n different letters and their connexion with general magic squares, Proc. London Math. Soc., 17 (1917), 25-41.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.8.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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E.g.f.: (1-x)^(-1/2)*exp(-x/2+x^2/4).
a(n)=(n-1)(a(n-1)+a(n-2))-(n-1)(n-2)a(n-3)/2.
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CROSSREFS
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Cf. A000985, A000986.
Adjacent sequences: A002134 A002135 A002136 this_sequence A002138 A002139 A002140
Sequence in context: A027296 A151495 A009358 this_sequence A009361 A075759 A000993
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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