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A302658
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Number of minimal total dominating sets in the wheel graph on n nodes.
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0
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1, 2, 6, 8, 10, 15, 14, 12, 21, 35, 33, 37, 52, 63, 83, 116, 136, 162, 228, 309, 388, 506, 667, 865, 1155, 1547, 2010, 2629, 3509, 4654, 6138, 8132, 10750, 14195, 18842, 25000, 33041, 43719, 57957, 76769, 101680, 134731, 178407, 236240, 313052, 414782, 549336
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OFFSET
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2,2
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COMMENTS
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Wheel graphs are defined for n>=4; extended to n=2 using formula. - Andrew Howroyd, Apr 15 2018
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LINKS
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Table of n, a(n) for n=2..48.
Eric Weisstein's World of Mathematics, Total Dominating Set
Eric Weisstein's World of Mathematics, Wheel Graph
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1,0,0,-1,0,1,1,-1).
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FORMULA
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a(n) = A300738(n-1) + (n-1). - Andrew Howroyd, Apr 15 2018
G.f.: x^2*(1 + 3*x^2 - 3*x^3 - x^4 - x^5 - 8*x^6 - 2*x^7 + 8*x^8 + 11*x^9 - 9*x^10)/((-1 + x)^2*(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)).
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MATHEMATICA
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Table[n - 1 + RootSum[-1 - # + #^3 &, #^(n - 1) &] + (1 - (-1)^n) RootSum[-1 + #^2 + #^3 &, #^((n - 1)/2) &], {n, 2, 50}]
LinearRecurrence[{2, -1, 1, -1, 0, 0, -1, 0, 1, 1, -1}, {1, 2, 6, 8, 10, 15, 14, 12, 21, 35, 33}, 50]
CoefficientList[Series[(1 + 3 x^2 - 3 x^3 - x^4 - x^5 - 8 x^6 - 2 x^7 + 8 x^8 + 11 x^9 - 9 x^10)/((-1 + x)^2 (1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)), {x, 0, 50}], x]
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PROG
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(PARI) {my(v=concat([0, 0], Vec((3 + 4*x + 5*x^2 + 6*x^3 - 8*x^5 - 9*x^6)/((1 - x^2 - x^3)*(1 + x^2 - x^6)) + O(x^50)))); vector(#v, i, v[i]+i)} \\ Andrew Howroyd, Apr 15 2018
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CROSSREFS
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Cf. A213661, A290270, A300738, A302603.
Sequence in context: A036554 A260400 A296387 * A324175 A084909 A038619
Adjacent sequences: A302655 A302656 A302657 * A302659 A302660 A302661
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KEYWORD
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nonn
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AUTHOR
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Eric W. Weisstein, Apr 11 2018
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EXTENSIONS
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a(2)-a(3) and terms a(20) and beyond from Andrew Howroyd, Apr 15 2018
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STATUS
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approved
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