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A297713
Number of minimal edge covers in the n-dipyramidal graph.
3
1, 6, 24, 74, 180, 464, 1113, 2646, 6360, 15222, 36795, 89584, 219635, 542320, 1346881, 3361998, 8427172, 21195416, 53455740, 135112332, 342093443, 867325032, 2201286622, 5591469852, 14211796995, 36139507614, 91934054637, 233934039872, 595393224041, 1515602413390
OFFSET
1,2
COMMENTS
Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, Jun 26 2018
LINKS
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Minimal Edge Cover
Index entries for linear recurrences with constant coefficients, signature (4, 1, -12, -15, 24, 49, 6, -73, -76, 5, 80, 72, 14, -30, -34, -19, -6, -1).
FORMULA
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
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
MATHEMATICA
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]
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]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 18 2018
EXTENSIONS
a(1)-a(2) and terms a(9) and beyond from Andrew Howroyd, Jun 26 2018
STATUS
approved