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A303046
Number of minimum total dominating sets in the n-Moebius ladder.
3
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
OFFSET
1,2
COMMENTS
Sequence extrapolated to n = 1 using recurrence. - Andrew Howroyd, Apr 18 2018
LINKS
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).
FORMULA
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
MATHEMATICA
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]
PROG
(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
CROSSREFS
Sequence in context: A200105 A153268 A197847 * A155554 A347217 A019902
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 17 2018
EXTENSIONS
a(1)-a(2) and terms a(14) and beyond from Andrew Howroyd, Apr 18 2018
STATUS
approved