A378701 Number of minimal edge covers in the n-Plummer-Toft graph.

25, 66, 181, 456, 1075, 2579, 6082, 14414, 34450, 82895, 201315, 492855, 1215426, 3016505, 7526261, 18860558, 47431375, 119619948, 302351431, 765563707, 1941079274, 4926790178, 12515217136, 31811484793, 80897818405, 205801073727, 523695045908, 1332908173773

Offset

1,1

Links

Christian Sievers, Table of n, a(n) for n = 1..2461

Eric Weisstein's World of Mathematics, Minimal Edge Cover.

Eric Weisstein's World of Mathematics, Plummer-Toft Graph.

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

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, Dec 09 2024

G.f.: x*(25-34*x-108*x^2-34*x^3+237*x^4+385*x^5+69*x^6-481*x^7-599*x^8-162*x^9+280*x^10+235*x^11-101*x^12-322*x^13-285*x^14-146*x^15-44*x^16-7*x^17)/((-1+x^2+x^3)^3*(-1+x+x^2+x^3)^2*(-1+2*x+x^2+x^3)). - Eric W. Weisstein, Dec 09 2024

Mathematica

LinearRecurrence[{4, 1, -12, -15, 24, 49, 6, -73, -76, 5, 80, 72, 14, -30, -34, -19, -6, -1}, {25, 66, 181, 456, 1075, 2579, 6082, 14414, 34450, 82895, 201315, 492855, 1215426, 3016505, 7526261, 18860558, 47431375, 119619948}, 20] (* Eric W. Weisstein, Dec 09 2024 *)
CoefficientList[Series[(25 - 34 x - 108 x^2 - 34 x^3 + 237 x^4 + 385 x^5 + 69 x^6 - 481 x^7 - 599 x^8 - 162 x^9 + 280 x^10 + 235 x^11 - 101 x^12 - 322 x^13 - 285 x^14 - 146 x^15 - 44 x^16 - 7 x^17)/((-1 + x^2 + x^3)^3 (-1 + x + x^2 + x^3)^2 (-1 + 2 x + x^2 + x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 09 2024 *)

Crossrefs

Sequence in context: A211462 A350233 A278855 * A137186 A109676 A223888

Adjacent sequences: A378697 A378699 A378700 * A378704 A378706 A378707

Keyword

nonn,easy,new

Author

Eric W. Weisstein, Dec 04 2024

Extensions

a(8) and beyond from Christian Sievers, Dec 08 2024

Status

approved