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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
OFFSET
3,1
LINKS
Eric Weisstein's World of Mathematics, Cycle Graph
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
KEYWORD
nonn,easy
AUTHOR
Andrew Howroyd, Sep 11 2019
STATUS
approved