A379182 Number of minimal edge covers in the n-double cone graph.
0, 1, 21, 58, 149, 566, 1676, 5482, 18021, 59665, 199700, 670517, 2259384, 7624878, 25759564, 87078065, 294452965, 995889190, 3368616437, 11395096538, 38547768152, 130403228310, 441145535869, 1492374662977, 5048648849760, 17079422831941, 57779211419220, 195465558240778
Offset: 0
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..200
- Eric Weisstein's World of Mathematics, Double Cone Graph.
- Eric Weisstein's World of Mathematics, Minimal Edge Cover.
- Index entries for linear recurrences with constant coefficients, signature (4,0,-2,-21,8,8,34,-12,20,-28,6,-24,20,-13,12,-4,2,-1).
Programs
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PARI
seq(n)={my(g1 = 1/(1-x -x^2 - x^3) + O(x*x^n), g2 = 1/(1-x^2-x^3) + O(x*x^n), h1 = g1 + x^2*g1 + 2*x^3*g1, h2 = g2 + x^2*g2 + 2*x^3*g2); Vec(serconvol(h1,h1) - serconvol(h2,h2) + 2*serconvol(h2, x*deriv(2*x^2*g2 + x^3*g2)), -n-1)} \\ Andrew Howroyd, Dec 18 2024
Formula
G.f.: x*(1 + 17*x - 26*x^2 - 81*x^3 + 33*x^4 - 39*x^5 + 118*x^6 - 312*x^7 + 461*x^8 - 260*x^9 + 183*x^10 - 211*x^11 + 33*x^12 + 10*x^13 + 3*x^14 - 2*x^16)/((1 + x + x^2 - x^3)*(1 + x - x^3)^2*(1 - 2*x + x^2 - x^3)^2*(1 - 3*x - x^2 - x^3)). - Andrew Howroyd, Dec 18 2024
Extensions
a(0)-a(2) prepended and a(8) onwards from Andrew Howroyd, Dec 18 2024
Comments