A303148 Number of minimal total dominating sets in the n-pan graph.
1, 1, 3, 2, 4, 8, 6, 6, 13, 18, 20, 28, 37, 45, 65, 91, 111, 144, 200, 264, 346, 464, 609, 798, 1072, 1428, 1873, 2479, 3297, 4361, 5779, 7670, 10140, 13416, 17806, 23598, 31229, 41374, 54820, 72600, 96197, 127465, 168801, 223587, 296255, 392460, 519856
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Eric Weisstein's World of Mathematics, Minimal Total Dominating Set.
- Eric Weisstein's World of Mathematics, Pan Graph.
- Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1,1,0,-1,-1).
Programs
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Mathematica
LinearRecurrence[{0, 0, 1, 1, 1, 1, 0, -1, -1}, {1, 1, 3, 2, 4, 8, 6, 6, 13}, 20] CoefficientList[Series[(1 + x + 3 x^2 + x^3 + 2 x^4 + 3 x^5 - x^6 - 4 x^7 - 3 x^8)/(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9), {x, 0, 20}], x] -
PARI
Vec((1 + x + 3*x^2 + x^3 + 2*x^4 + 3*x^5 - x^6 - 4*x^7 - 3*x^8)/((1 - x^2 - x^3)*(1 + x^2 - x^6)) + O(x^40)) \\ Andrew Howroyd, Apr 19 2018
Formula
From Andrew Howroyd, Apr 19 2018: (Start)
a(n) = a(n-3) + a(n-4) + a(n-5) + a(n-6) - a(n-8) - a(n-9) for n > 9.
G.f.: x*(1 + x + 3*x^2 + x^3 + 2*x^4 + 3*x^5 - x^6 - 4*x^7 - 3*x^8)/((1 - x^2 - x^3)*(1 + x^2 - x^6)). (End)
Extensions
a(1)-a(2) and terms a(20) and beyond from Andrew Howroyd, Apr 19 2018
Comments