Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #13 Jun 28 2018 04:51:33
%S 1,6,24,74,180,464,1113,2646,6360,15222,36795,89584,219635,542320,
%T 1346881,3361998,8427172,21195416,53455740,135112332,342093443,
%U 867325032,2201286622,5591469852,14211796995,36139507614,91934054637,233934039872,595393224041,1515602413390
%N Number of minimal edge covers in the n-dipyramidal graph.
%C Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, Jun 26 2018
%H Andrew Howroyd, <a href="/A297713/b297713.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalEdgeCover.html">Minimal Edge Cover</a>
%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (4, 1, -12, -15, 24, 49, 6, -73, -76, 5, 80, 72, 14, -30, -34, -19, -6, -1).
%F G.f.: x*(1 + x)*(1 + x - 2*x^2 - 14*x^3 - 39*x^4 + 63*x^5 + 69*x^6 + 55*x^7 - 39*x^8 - 85*x^9 - 118*x^10 - 102*x^11 - 63*x^12 - 27*x^13 - 7*x^14 - x^15)/((1 - x^2 - x^3)^3*(1 - x - x^2 - x^3)^2*(1 - 2*x - x^2 - x^3)). - _Andrew Howroyd_, Jun 26 2018
%F a(n) = 4*a(n-1) + a(n-2) - 12*a(n-3) - 15*a(n-4) + 24*a(n-5) + 49*a(n-6) + 6*a(n-7) - 73*a(n-8) - 76*a(n-9) + 5*a(n-10) + 80*a(n-11) + 72*a(n-12) + 14*a(n-13) - 30*a(n-14) - 34*a(n-15) - 19*a(n-16) - 6*a(n-17) - a(n-18). - _Eric W. Weisstein_, Jun 27 2018
%t LinearRecurrence[{4, 1, -12, -15, 24, 49, 6, -73, -76, 5, 80, 72, 14, -30, -34, -19, -6, -1}, {1, 6, 24, 74, 180, 464, 1113, 2646, 6360, 15222, 36795, 89584, 219635, 542320, 1346881, 3361998, 8427172, 21195416}, 30]
%t CoefficientList[Series[-(1 + x) (-1 - x + 2 x^2 + 14 x^3 + 39 x^4 - 63 x^5 - 69 x^6 - 55 x^7 + 39 x^8 + 85 x^9 + 118 x^10 + 102 x^11 + 63 x^12 + 27 x^13 + 7 x^14 + x^15)/((-1 + x^2 + x^3)^3 (-1 + x + x^2 + x^3)^2 (-1 + 2 x + x^2 + x^3)), {x, 0, 20}], x]
%o (PARI) Vec((1 + x)*(1 + x - 2*x^2 - 14*x^3 - 39*x^4 + 63*x^5 + 69*x^6 + 55*x^7 - 39*x^8 - 85*x^9 - 118*x^10 - 102*x^11 - 63*x^12 - 27*x^13 - 7*x^14 - x^15)/((1 - x^2 - x^3)^3*(1 - x - x^2 - x^3)^2*(1 - 2*x - x^2 - x^3)) + O(x^40)) \\ _Andrew Howroyd_, Jun 26 2018
%Y Cf. A296995, A297064, A298822.
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Jun 18 2018
%E a(1)-a(2) and terms a(9) and beyond from _Andrew Howroyd_, Jun 26 2018