A297713 Number of minimal edge covers in the n-dipyramidal graph.

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

Andrew Howroyd, Table of n, a(n) for n = 1..200

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

Cf. A296995, A297064, A298822.

Sequence in context: A090574 A294842 A290132 * A225383 A257956 A341364

Adjacent sequences: A297710 A297711 A297712 * A297714 A297715 A297716

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