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A302946
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Number of minimal (and minimum) total dominating sets in the 2n-crossed prism graph.
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3
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4, 36, 196, 1156, 6724, 39204, 228484, 1331716, 7761796, 45239076, 263672644, 1536796804, 8957108164, 52205852196, 304278004996, 1773462177796, 10336495061764, 60245508192804, 351136554095044, 2046573816377476, 11928306344169796, 69523264248641316
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OFFSET
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1,1
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COMMENTS
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Extended to a(1) using the formula/recurrence.
Since minimal and minimum total dominating sets are equivalent, the crossed prism graphs could be said to be "well totally dominated".
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LINKS
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FORMULA
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a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3).
G.f.: 4*x*(1 + 4*x - x^2)/((1 + x)*(1 - 6*x + x^2)).
a(n) = 4*(-1)^n*chebyshevT(n,i)^2, where i is the imaginary unit. - Eric W. Weisstein, Apr 17 2018
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MATHEMATICA
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Table[2 (ChebyshevT[n, 3] + (-1)^n), {n, 20}]
Table[4 (-1)^n ChebyshevT[n, I]^2, {n, 20}]
LinearRecurrence[{5, 5, -1}, {4, 36, 196}, 20]
CoefficientList[Series[-4 (-1 - 4 x + x^2)/(1 - 5 x - 5 x^2 + x^3), {x, 0, 20}], x]
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PROG
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(PARI) Vec(4*(1 + 4*x - x^2)/((1 + x)*(1 - 6*x + x^2)) + O(x^30)) \\ Andrew Howroyd, Apr 16 2018
(PARI) a(n) = 2*(polchebyshev(n, 1, 3) + (-1)^n); \\ Michel Marcus, Apr 17 2018
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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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