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A302763
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Number of minimal total dominating sets in the n-antiprism graph.
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4
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0, 4, 12, 28, 80, 52, 203, 524, 903, 2184, 3960, 9628, 20735, 41619, 93392, 194732, 425901, 908791, 1923408, 4177488, 8887289, 19098160, 40895771, 87444572, 187934955, 401853599, 861531618, 1846051011, 3953574901, 8476042452, 18151661911, 38898045292
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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. - Andrew Howroyd, Apr 15 2018
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,2,4,5,8,-12,-23,-11,-11,8,37,23,-4,2,-7,-17,7,-7,-13,3,-1,-2,1).
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FORMULA
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G.f.: x^2*(4 + 12*x + 20*x^2 + 40*x^3 - 72*x^4 - 161*x^5 - 88*x^6 - 99*x^7 + 80*x^8 + 407*x^9 + 276*x^10 - 52*x^11 + 28*x^12 - 105*x^13 - 272*x^14 + 119*x^15 - 126*x^16 - 247*x^17 + 60*x^18 - 21*x^19 - 44*x^20 + 23*x^21)/(1 - 2*x^2 - 4*x^3 - 5*x^4 - 8*x^5 + 12*x^6 + 23*x^7 + 11*x^8 + 11*x^9 - 8*x^10 - 37*x^11 - 23*x^12 + 4*x^13 - 2*x^14 + 7*x^15 + 17*x^16 - 7*x^17 + 7*x^18 + 13*x^19 - 3*x^20 + x^21 + 2*x^22 - x^23). - Andrew Howroyd, Apr 15 2018
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MATHEMATICA
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Table[RootSum[-1 + 2 # + #^2 - 3 #^3 + 13 #^4 + 7 #^5 - 7 #^6 + 17 #^7 + 7 #^8 - 2 #^9 + 4 #^10 - 23 #^11 - 37 #^12 - 8 #^13 + 11 #^14 + 11 #^15 + 23 #^16 + 12 #^17 - 8 #^18 - 5 #^19 - 4 #^20 - 2 #^21 + #^23 &, #^n &], {n, 30}]
RootSum[-1 + 2 # + #^2 - 3 #^3 + 13 #^4 + 7 #^5 - 7 #^6 + 17 #^7 + 7 #^8 - 2 #^9 + 4 #^10 - 23 #^11 - 37 #^12 - 8 #^13 + 11 #^14 + 11 #^15 + 23 #^16 + 12 #^17 - 8 #^18 - 5 #^19 - 4 #^20 - 2 #^21 + #^23 &, #^Range[30] &]
LinearRecurrence[{0, 2, 4, 5, 8, -12, -23, -11, -11, 8, 37, 23, -4, 2, -7, -17, 7, -7, -13, 3, -1, -2, 1}, {0, 4, 12, 28, 80, 52, 203, 524, 903, 2184, 3960, 9628, 20735, 41619, 93392, 194732, 425901, 908791, 1923408, 4177488, 8887289, 19098160, 40895771}, 40]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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