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A286185
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Number of connected induced (non-null) subgraphs of the Möbius ladder graph with 2n nodes.
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16
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3, 15, 55, 173, 511, 1451, 4019, 10937, 29371, 78055, 205679, 538149, 1399607, 3621315, 9327723, 23931633, 61186163, 155949119, 396369831, 1004904733, 2541896559, 6416348251, 16165611043, 40657256617, 102090514731, 255968753175, 640899345631, 1602640560533
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 6*a(n-1) - 11*a(n-2) + 4*a(n-3) + 5*a(n-4) - 2*a(n-5) - a(n-6), for n>6 (conjectured).
a(n) = 1/4*((1-sqrt(2))^n*(4-3*sqrt(2)*n) + (1+sqrt(2))^n*(4+3*sqrt(2)*n)) - 1 - n (conjectured). - Eric W. Weisstein, May 08 2017
a(n) = Lucas(n, 2) + 3*n*Fibonacci(n, 2) - n - 1, where Lucas(n, 2) = A002203(n) and Fibonacci(n, 2) = A000129(n) (conjectured). - Eric W. Weisstein, May 08 2017
G.f. (subject to the above conjectures. In fact all three conjectures are equivalent): (3*x-3*x^2-2*x^3-4*x^4+3*x^5-x^6)/(1-3*x+x^2+x^3)^2. - Robert Israel, May 08 2017
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MATHEMATICA
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a[n_] := Block[{g = CirculantGraph[2 n, {1, n}]}, -1 + ParallelSum[ Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@ Range[2 n]}]]; Array[a, 8]
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CROSSREFS
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Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen).
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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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