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A303162
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Number of minimal total dominating sets in the n-Moebius ladder.
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1
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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
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OFFSET
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1,2
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COMMENTS
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Sequence extrapolated to n=1 using recurrence.
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LINKS
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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).
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FORMULA
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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
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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