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A292056 Wiener index of the n-Keller graph. 3
12, 200, 2944, 43392, 650240, 9889792, 152174592, 2362671104, 36940546048, 580718690304, 9167616081920, 145195622465536, 2305296785473536, 36670757861851136, 584164270070038528, 9315814196367065088, 148683258271895650304, 2374494908625021042688 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Keller graph is connected for n >= 2.

The n-Keller graph is distance regular with 4^n vertices and for n > 1 the radius is 2. The degree of each vertex is 4^n - 3^n - n. Sequence extrapolated to n = 1 using formula. (The Keller graph is disconnected for n = 1, so a(1) is not the Wiener index of that graph.) - Andrew Howroyd, Sep 08 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Keller Graph

Eric Weisstein's World of Mathematics, Wiener Index

Index entries for linear recurrences with constant coefficients, signature (36,-432,1984,-3072).

FORMULA

a(n) = 4^n * (4^n + 3^n + n - 2) / 2. - Andrew Howroyd, Sep 08 2017

a(n) = 36*a(n-1) - 432*a(n-2) + 1984*a(n-3) - 3072*a(n-4).

G.f.: -((8 x (-25 + 532 x - 2976 x^2 + 4608 x^3))/((-1 + 4 x)^2 (1 - 28 x + 192 x^2))).

E.g.f.: exp(4*x)*(exp(8*x) + exp(12*x) + 4*x - 2)/2. - Stefano Spezia, Sep 02 2022

MATHEMATICA

Table[4^n (4^n + 3^n + n - 2)/2, {n, 20}]

LinearRecurrence[{36, -432, 1984, -3072}, {12, 200, 2944, 43392}, 20]

CoefficientList[Series[-((8 (-25 + 532 x - 2976 x^2 + 4608 x^3))/((-1 + 4 x)^2 (1 - 28 x + 192 x^2))), {x, 0, 20}], x]

PROG

(PARI) a(n) = 4^n * (4^n + 3^n + n - 2) / 2; \\ Andrew Howroyd, Sep 08 2017

CROSSREFS

Sequence in context: A036240 A346509 A355127 * A277311 A327073 A133242

Adjacent sequences:  A292053 A292054 A292055 * A292057 A292058 A292059

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Sep 08 2017

EXTENSIONS

Terms a(7) and beyond from Andrew Howroyd, Sep 08 2017

STATUS

approved

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Last modified October 6 19:00 EDT 2022. Contains 357270 sequences. (Running on oeis4.)