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A347559 Number of minimum dominating sets in the n-Moebius ladder. 0
9, 24, 10, 4, 14, 80, 18, 4, 22, 168, 26, 4, 30, 288, 34, 4, 38, 440, 42, 4, 46, 624, 50, 4, 54, 840, 58, 4, 62, 1088, 66, 4, 70, 1368, 74, 4, 78, 1680, 82, 4, 86, 2024, 90, 4, 94, 2400, 98, 4, 102, 2808, 106, 4, 110, 3248, 114, 4, 118, 3720, 122, 4, 126, 4224 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Table of n, a(n) for n=3..64.

Eric Weisstein's World of Mathematics, Minimum Dominating Set

Eric Weisstein's World of Mathematics, Moebius Ladder

Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

FORMULA

a(n) = n*(n+2) for n == 0 (mod 4).

a(n) = 2*n for n == 1 (mod 2) and n > 3.

a(n) = 4 for n == 2 (mod 4).

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12) for n > 3.

G.f.: x^3*(-9 - 24*x - 10*x^2 - 4*x^3 + 13*x^4 - 8*x^5 + 12*x^6 + 8*x^7 - 7*x^8 - 2*x^10 - 4*x^11 + 3*x^12)/((-1 + x)^3*(1 + x)^3*(1 + x^2)^3).

MATHEMATICA

Table[Piecewise[{{9, n == 3}, {n (n + 2), Mod[n, 4] == 0}, {2 n, Mod[n, 2] == 1}, {4, Mod[n, 4] == 2}}, 0], {n, 3, 20}]

Join[{9}, LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {24, 10, 4, 14, 80, 18, 4, 22, 168, 26, 4, 30}, 20]]

CoefficientList[Series[(-9 - 24 x - 10 x^2 - 4 x^3 + 13 x^4 - 8 x^5 + 12 x^6 + 8 x^7 - 7 x^8 - 2 x^10 - 4 x^11 + 3 x^12)/((-1 + x)^3 (1 + x)^3 (1 + x^2)^3), {x, 0, 20}], x]

CROSSREFS

Cf. A284663, A290337.

Sequence in context: A066008 A101058 A247960 * A161431 A223379 A223297

Adjacent sequences:  A347556 A347557 A347558 * A347560 A347561 A347562

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Sep 06 2021

STATUS

approved

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Last modified January 27 16:33 EST 2022. Contains 350609 sequences. (Running on oeis4.)