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A033440
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Number of edges in 8-partite Turan graph of order n.
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10
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0, 0, 1, 3, 6, 10, 15, 21, 28, 35, 43, 52, 62, 73, 85, 98, 112, 126, 141, 157, 174, 192, 211, 231, 252, 273, 295, 318, 342, 367, 393, 420, 448, 476, 505, 535, 566, 598, 631, 665, 700, 735, 771, 808, 846, 885, 925
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OFFSET
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0,4
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REFERENCES
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Graham et al., Handbook of Combinatorics, Vol. 2, p. 1234.
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LINKS
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Table of n, a(n) for n=0..46.
Wikipedia, Tur%C3%A1n graph [From Reinhard Zumkeller, Nov 30 2009]
Eric Weisstein's World of Mathematics, Tur%C3%A1n Graph [From Reinhard Zumkeller, Nov 30 2009]
Index to sequences with linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,1,-2,1).
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FORMULA
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a(n)=round( (7/16)*n(n-2) ) +0 or -1 depending on n: if there is k such 8k+4<=n<=8k+6 then a(n) = floor( (7/16)*n*(n-2)) otherwise a(n) = round( (7/16)*n(n-2)). E.g. because 8*2+4<=21<=8*2+6 a(n)=floor((7/16)*21*19)=floor(174, 5625)=174. - Benoit Cloitre, Jan 17 2002
a(n) = sum(0<=k<=n, A168181(k)*(n-k) ). [From Reinhard Zumkeller, Nov 30 2009]
G.f. -x^2*(x^6+x^5+x^4+x^3+x^2+x+1)/((x-1)^3*(x+1)*(x^2+1)*(x^4+1)). [Colin Barker, Aug 09 2012]
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CROSSREFS
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Cf. A002620, A000212, A033436, A033437, A033438, A033439, A033441, A033442, A033443, A033444. [From Reinhard Zumkeller, Nov 30 2009]
Sequence in context: A161208 A109444 A124157 * A067525 A130487 A108923
Adjacent sequences: A033437 A033438 A033439 * A033441 A033442 A033443
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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