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A055503
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Take n points in general position in plane; draw all lines joining them; sequence gives number of connected regions formed.
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3
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1, 1, 2, 7, 18, 41, 85, 162, 287, 478, 756, 1145, 1672, 2367, 3263, 4396, 5805, 7532, 9622, 12123, 15086, 18565, 22617, 27302, 32683, 38826, 45800, 53677, 62532, 72443, 83491, 95760, 109337, 124312, 140778, 158831, 178570, 200097
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, Problem 1, p. 72; and Problem 8, p. 74.
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LINKS
| Author?, Title? (from Alexander Evnin (graph98(AT)yandex.ru), Dec 06 2008)
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FORMULA
| (1/8)*(n-1)*(n^3-5*n^2+18*n-8) for n>1.
for n>1: a(0)=2, a(1)=7, a(2)=18, a(3)=41, a(4)=85, a(n)=5a(n-1)- 10a(n-2)+ 10a(n-3)-5a(n-4)+a(n-5) [From Harvey P. Dale, May 06 2011]
for n>1, G.f.: (-2+3x-3x^2-x^3)/(-1+x)^5 [From Harvey P. Dale, May 06 2011]
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MAPLE
| A055503 := n->(1/8)*(n^4-6*n^3+23*n^2-26*n+8); [for n >1]
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MATHEMATICA
| Join[{1, 1}, Table[(1/8)(n-1)(n^3-5n^2+18n-8), {n, 2, 80}]] (* From Harvey P. Dale, May 06 2011 *)
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CROSSREFS
| Cf. A000124.
Sequence in context: A051743 A054111 A192955 * A077802 A095151 A147611
Adjacent sequences: A055500 A055501 A055502 * A055504 A055505 A055506
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jul 10 2000
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EXTENSIONS
| a(1) changed from 0 to 1 by N. J. A. Sloane (njas(AT)research.att.com), Dec 07 2008
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