A326347 Number of unordered pairs of 4-colorings of an n-cycle that differ in the coloring of exactly one vertex.

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

Author

Andrew Howroyd, Sep 11 2019

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A046717, A218034, A309380.

Programs

PARI

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

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).