A303212 Number of minimum total dominating sets in the n X n rook complement graph.
0, 1, 6, 96, 600, 2400, 7350, 18816, 42336, 86400, 163350, 290400, 490776, 794976, 1242150, 1881600, 2774400, 3995136, 5633766, 7797600, 10613400, 14229600, 18818646, 24579456, 31740000, 40560000, 51333750, 64393056, 80110296, 98901600
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Eric Weisstein's World of Mathematics, Rook Complement Graph.
- Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Mathematica
Table[If[n == 2, 1, 6 Binomial[n, 3]^2], {n, 20}] Join[{0, 1}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 6, 96, 600, 2400, 7350}, {3, 20}]] CoefficientList[Series[x (-1 + x - 75 x^2 - 19 x^3 - 41 x^4 + 21 x^5 - 7 x^6 + x^7)/(-1 + x)^7, {x, 0, 20}], x] -
PARI
a(n) = if(n<3, n==2, 6*binomial(n,3)^2) \\ Andrew Howroyd, Apr 20 2018
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PARI
concat(0, Vec(x^2*(1 - x + 75*x^2 + 19*x^3 + 41*x^4 - 21*x^5 + 7*x^6 - x^7) / (1 - x)^7 + O(x^60))) \\ Colin Barker, Apr 20 2018
Formula
a(n) = A179058(n) for n > 2. - Andrew Howroyd, Apr 20 2018
From Colin Barker, Apr 20 2018: (Start)
G.f.: x^2*(1 - x + 75*x^2 + 19*x^3 + 41*x^4 - 21*x^5 + 7*x^6 - x^7) / (1 - x)^7.
a(n) = n^2*(2 - 3*n + n^2)^2 / 6 for n > 2.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 9.
(End)
Extensions
a(6)-a(30) from Andrew Howroyd, Apr 20 2018
Comments