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A303046
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Number of minimum total dominating sets in the n-Moebius ladder.
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3
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1, 6, 9, 8, 25, 3, 196, 56, 9, 20, 121, 3, 1521, 154, 9, 32, 289, 3, 5776, 300, 9, 44, 529, 3, 15625, 494, 9, 56, 841, 3, 34596, 736, 9, 68, 1225, 3, 67081, 1026, 9, 80, 1681, 3, 118336, 1364, 9, 92, 2209, 3, 194481, 1750, 9, 104, 2809, 3, 302500, 2184, 9
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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 18 2018
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Moebius Ladder
Eric Weisstein's World of Mathematics, Total Dominating Set
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,5,0,0,0,0,0,-10,0,0,0,0,0,10,0,0,0,0,0,-5,0,0,0,0,0,1).
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FORMULA
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From Andrew Howroyd, Apr 18 2018: (Start)
a(n) = 5*a(n-6) - 10*a(n-12) + 10*a(n-18) - 5*a(n-24) + a(n-30) for n > 30.
a(6k) = 3, a(6k+1) = (6*k+1)^2*(k+1)^2, a(6k+2) = (6*k+2)*(4*k+3), a(6k+3) = 9, a(6k+4) = (6*k+4)*2, a(6k+5) = (6*k+5)^2. (End)
a(3k) = 6 - 3*(-1)^k. - Eric W. Weisstein, Apr 19 2018
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MATHEMATICA
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Table[Piecewise[{{3, Mod[n, 6] == 0}, {(n (n + 5)/6)^2, Mod[n, 6] == 1}, {n (2 n + 5)/3, Mod[n, 6] == 2}, {9, Mod[n, 6] == 3}, {2 n, Mod[n, 6] == 4}, {n^2, Mod[n, 6] == 5}}], {n, 200}]
LinearRecurrence[{0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 1}, {1, 6, 9, 8, 25, 3, 196, 56, 9, 20, 121, 3, 1521, 154, 9, 32, 289, 3, 5776, 300, 9, 44, 529, 3, 15625, 494, 9, 56, 841, 3}, 200]
Rest @ CoefficientList[Series[3 x^6/(1 - x^6) - 9 x^3/(-1 + x^6) + 4 x^4 (2 + x^6)/(-1 + x^6)^2 - x^5 (25 + 46 x^6 + x^12)/(-1 + x^6)^3 - 2 x^2 (3 + 19 x^6 + 2 x^12)/(-1 + x^6)^3 - x (1 + 191 x^6 + 551 x^12 + 121 x^18)/(-1 + x^6)^5, {x, 0, 200}], x]
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PROG
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(PARI) a(n)=my(k=n\6, r=n%6); if(r<3, if(r==0, 3, if(r==1, n^2*(k+1)^2, n*(4*k+3))), if(r==3, 9, if(r==4, 2*n, n^2))) \\ Andrew Howroyd, Apr 18 2018
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CROSSREFS
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Cf. A295420, A302404.
Sequence in context: A200105 A153268 A197847 * A155554 A019902 A021147
Adjacent sequences: A303043 A303044 A303045 * A303047 A303048 A303049
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein, Apr 17 2018
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EXTENSIONS
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a(1)-a(2) and terms a(14) and beyond from Andrew Howroyd, Apr 18 2018
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STATUS
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approved
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