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A228317 The hyper-Wiener index of the triangular graph T(n) (n>=1). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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, 4 (see the Brualdi et al. reference, Theorem 5.2.4).

REFERENCES

R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press, 1992.

LINKS

Table of n, a(n) for n=1..38.

Eric Weisstein's World of Mathematics, TriangularGraph.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = n*(n-1)*(n-2)*(3*n-5)/8.

G.f.: 3*x^3*(1+2x)/(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). - R. J. Mathar, Mar 05 2017

MAPLE

a := proc (n) options operator, arrow: (1/8)*n*(n-1)*(n-2)*(3*n-5) end proc: seq(a(n), n = 1 .. 38);

CROSSREFS

Cf. A006011

Sequence in context: A281008 A238193 A054646 * A322228 A109721 A067002

Adjacent sequences:  A228314 A228315 A228316 * A228318 A228319 A228320

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Aug 26 2013

STATUS

approved

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Last modified February 15 21:12 EST 2019. Contains 320138 sequences. (Running on oeis4.)