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A326347 Number of unordered pairs of 4-colorings of an n-cycle that differ in the coloring of exactly one vertex. 2
36, 240, 780, 2952, 10164, 35040, 118044, 393720, 1299012, 4251600, 13817388, 44641128, 143488980, 459165120, 1463588412, 4649045976, 14721978468, 46490458800, 146444944716, 460255541064, 1443528741876, 4518872583840, 14121476823900, 44059007691192 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..200

Eric Weisstein's World of Mathematics, Cycle Graph

Index entries for linear recurrences with constant coefficients, signature (4,2,-12,-9).

FORMULA

a(n) = n*(3*A218034(n-2) + A218034(n-1)).

a(n) = 6*n*(3^(n-2) + (-1)^n).

a(n) = 12*n*A046717(n-2).

a(n) = 4*a(n-1) + 2*a(n-2) - 12*a(n-3) - 9*a(n-4) for n > 6.

G.f.: 12*x^3*(3 + 8*x - 21*x^2 - 18*x^3)/((1 + x)^2*(1 - 3*x)^2).

PROG

(PARI) a(n) = 6*n*(3^(n-2) + (-1)^n);

CROSSREFS

Cf. A046717, A218034, A309380.

Sequence in context: A297656 A268794 A159921 * A129149 A223558 A074363

Adjacent sequences:  A326344 A326345 A326346 * A326348 A326349 A326350

KEYWORD

nonn,easy

AUTHOR

Andrew Howroyd, Sep 11 2019

STATUS

approved

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Last modified March 30 06:59 EDT 2020. Contains 333119 sequences. (Running on oeis4.)