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Search: id:A005217
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| A005217 |
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Number of unlabeled unit interval graphs with n nodes.
(Formerly M1186)
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+0
2
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| 1, 2, 4, 9, 21, 55, 151, 447, 1389, 4502, 15046, 51505, 179463, 634086, 2265014, 8163125, 29637903, 108282989, 397761507, 1468063369, 5441174511, 20242989728, 75566702558, 282959337159, 1062523000005, 4000108867555, 15095081362907, 57088782570433
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.7.
Hanlon, Phil; Counting interval graphs. Trans. Amer. Math. Soc. 272 (1982), no. 2, 383-426.
R. W. Robinson, personal communication.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1980.
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LINKS
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R. W. Robinson, Table of n, a(n) for n = 1..190
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FORMULA
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G.f. A(x) = x + 2x^2 + 4x^3 + 9x^4 + 21x^5 + ... satisfies 1 + A(x) = exp( Sum_{k >= 1} psi(x^k)/k ), where psi(x) = (1+2*x-sqrt(1-4*x)*sqrt(1-4*x^2))/(4*sqrt(1-4*x^2)) is the g.f. for A007123.
For asymptotics, see for example Finch.
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CROSSREFS
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Adjacent sequences: A005214 A005215 A005216 this_sequence A005218 A005219 A005220
Sequence in context: A063026 A106219 A032129 this_sequence A001430 A057513 A006080
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KEYWORD
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nonn
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AUTHOR
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njas
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