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A228317
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The hyper-Wiener index of the triangular graph T(n) (n >= 1).
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2
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0, 0, 3, 21, 75, 195, 420, 798, 1386, 2250, 3465, 5115, 7293, 10101, 13650, 18060, 23460, 29988, 37791, 47025, 57855, 70455, 85008, 101706, 120750, 142350, 166725, 194103, 224721, 258825, 296670, 338520, 384648, 435336, 490875, 551565, 617715, 689643
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OFFSET
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1,3
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COMMENTS
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The triangular graph T(n) is the graph whose vertices represent the 2-subsets of {1,2,...,n} and two vertices are adjacent provided the corresponding 2-subsets have a nonempty intersection.
The triangular graph T(n) is a strongly regular graph with parameters n*(n-1)/2, 2*(n-2), n-2, and 4 (see the Brualdi and Ryser reference, Theorem 5.2.4).
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REFERENCES
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R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press, 1992.
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LINKS
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Table of n, a(n) for n=1..38.
G. G. Cash, Relationship between the Hosoya polynomial and the hyper-Wiener index, Applied Mathematics Letters, 15(7) (2002), 893-895.
Eric Weisstein's World of Mathematics, Triangular Graph.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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a(n) = n*(n - 1)*(n - 2)*(3*n - 5)/8.
G.f.: 3*x^3*(1 + 2*x)/(1 - x)^5.
The Hosoya-Wiener polynomial of T(n) is (1/8)*n*(n - 1)*(4 + 4*(n-2)*t + (n - 2)*(n - 3)*t^2).
a(n) = 3*A001296(n-2) for n >= 2. - R. J. Mathar, Mar 05 2017
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MAPLE
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a := proc (n) options operator, arrow: (1/8)*n*(n-1)*(n-2)*(3*n-5) end proc: seq(a(n), n = 1 .. 38);
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CROSSREFS
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Cf. A001296, A006011.
Sequence in context: A281008 A238193 A054646 * A322228 A109721 A067002
Adjacent sequences: A228314 A228315 A228316 * A228318 A228319 A228320
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KEYWORD
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nonn,easy
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AUTHOR
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Emeric Deutsch, Aug 26 2013
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STATUS
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approved
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