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A303162 Number of minimal total dominating sets in the n-Moebius ladder. 1
0, 6, 9, 14, 25, 57, 196, 222, 441, 851, 1936, 3281, 6084, 12662, 24964, 48830, 93636, 188265, 369664, 725859, 1423249, 2798582, 5503716, 10790049, 21206025, 41601462, 81703521, 160396110, 314991504, 618413702, 1214104336, 2384319102, 4681706929, 9192838950 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence extrapolated to n=1 using recurrence.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Moebius Ladder

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (2, -2, 3, 4, -7, 5, 0, -21, 39, -24, 21, 33, -36, 63, -33, 0, 33, -63, 36, -33, -21, 24, -39, 21, 0, -5, 7, -4, -3, 2, -2, 1).

FORMULA

G.f.: x^2*(6 - 3*x + 8*x^2 - 3*x^3 - 16*x^4 + 96*x^5 - 154*x^6 + 171*x^7 - 172*x^8 - 105*x^9 + 74*x^10 - 280*x^11 - 8*x^12 + 91*x^13 - 508*x^14 + 289*x^15 - 386*x^16 - 64*x^17 - 124*x^18 - 231*x^19 - 28*x^20 - 63*x^21 - 28*x^22 + 96*x^23 - 46*x^24 + 39*x^25 - 16*x^26 - 21*x^27 + 18*x^28 - 12*x^29 + 6*x^30)/((1 - x)*(1 + x)*(1 - 2*x - x^2 + 3*x^3 - x^4 - 2*x^5 + x^6)*(1 - 4*x + 10*x^2 - 19*x^3 + 28*x^4 - 34*x^5 + 37*x^6 - 34*x^7 + 28*x^8 - 19*x^9 + 10*x^10 - 4*x^11 + x^12)*(1 + 4*x + 10*x^2 + 19*x^3 + 28*x^4 + 34*x^5 + 37*x^6 + 34*x^7 + 28*x^8 + 19*x^9 + 10*x^10 + 4*x^11 + x^12)). - Andrew Howroyd, Apr 19 2018

MATHEMATICA

Table[3 - 3 (-1)^n + RootSum[1 - 2 # - #^2 + 3 #^3 - #^4 - 2 #^5 + #^6 &, #^n &] - RootSum[1 - 4 # + 10 #^2 - 19 #^3 + 28 #^4 - 34 #^5 + 37 #^6 - 34 #^7 + 28 #^8 - 19 #^9 + 10 #^10 - 4 #^11 + #^12 &, #^n &] + RootSum[1 + 4 # + 10 #^2 + 19 #^3 + 28 #^4 + 34 #^5 + 37 #^6 + 34 #^7 + 28 #^8 + 19 #^9 + 10 #^10 + 4 #^11 + #^12 &, #^n &], {n, 200}]

LinearRecurrence[{2, -2, 3, 4, -7, 5, 0, -21, 39, -24, 21, 33, -36,

  63, -33, 0, 33, -63, 36, -33, -21, 24, -39, 21, 0, -5, 7, -4, -3,

  2, -2, 1}, {0, 6, 9, 14, 25, 57, 196, 222, 441, 851, 1936, 3281,

  6084, 12662, 24964, 48830, 93636, 188265, 369664, 725859, 1423249,

  2798582, 5503716, 10790049, 21206025, 41601462, 81703521, 160396110, 314991504, 618413702, 1214104336, 2384319102}, 200]

Rest @ CoefficientList[Series[x^2 (6 - 3 x + 8 x^2 - 3 x^3 - 16 x^4 + 96 x^5 - 154 x^6 + 171 x^7 - 172 x^8 - 105 x^9 + 74 x^10 - 280 x^11 - 8 x^12 + 91 x^13 - 508 x^14 + 289 x^15 - 386 x^16 - 64 x^17 - 124 x^18 - 231 x^19 - 28 x^20 - 63 x^21 - 28 x^22 + 96 x^23 - 46 x^24 + 39 x^25 - 16 x^26 - 21 x^27 + 18 x^28 - 12 x^29 + 6 x^30)/((1 - x) (1 + x) (1 - 2 x - x^2 + 3 x^3 - x^4 - 2 x^5 + x^6) (1 - 4 x + 10 x^2 - 19 x^3 + 28 x^4 - 34 x^5 + 37 x^6 - 34 x^7 + 28 x^8 - 19 x^9 + 10 x^10 - 4 x^11 + x^12) (1 + 4 x + 10 x^2 + 19 x^3 + 28 x^4 + 34 x^5 + 37 x^6 + 34 x^7 + 28 x^8 + 19 x^9 + 10 x^10 + 4 x^11 + x^12)), {x, 0, 200}], x]

CROSSREFS

Cf. A284663, A290337, A295420, A303006, A303046.

Sequence in context: A300573 A020717 A196993 * A242042 A316021 A185398

Adjacent sequences:  A303159 A303160 A303161 * A303163 A303164 A303165

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 19 2018

EXTENSIONS

a(1)-a(2) and terms a(11) and beyond from Andrew Howroyd, Apr 19 2018

STATUS

approved

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Last modified July 24 05:07 EDT 2019. Contains 325290 sequences. (Running on oeis4.)