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

3,1

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