OFFSET
1,2
COMMENTS
The sequence has been extended to n=1 using the recurrence. - Andrew Howroyd, May 29 2025
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Minimal Edge Cover.
Eric Weisstein's World of Mathematics, Trapezohedral Graph.
Index entries for linear recurrences with constant coefficients, signature (13,-72,229,-489,797,-1075,1219,-1188,1028,-772,519,-315,158,-82,27,-13,2,-1).
FORMULA
G.f.: x*(1 - 4*x + 4*x^2 - 29*x^3 + 150*x^4 - 334*x^5 + 507*x^6 - 525*x^7 + 296*x^8 - 153*x^9 - 11*x^10 + 26*x^11 - 58*x^12 + 9*x^13 - 16*x^14 + 2*x^15 - x^16)/((1 - 2*x - x^3)^2*(1 - 2*x + x^2 - x^3)^3*(1 - 3*x - x^2 - x^3)). - Andrew Howroyd, May 29 2025
a(n) = 13*a(n-1)-72*a(n-2)+229*a(n-3)-489*a(n-4)+797*a(n-5)-1075*a(n-6)+1219*a(n-7)-1188*a(n-8)+1028*a(n-9)-772*a(n-10)+519*a(n-11)-315*a(n-12)+158*a(n-13)-82*a(n-14)+27*a(n-15)-13*a(n-16)+2*a(n-17)-a(n-18). - Eric W. Weisstein, Oct 01 2025
MATHEMATICA
LinearRecurrence[{13, -72, 229, -489, 797, -1075, 1219, -1188, 1028, -772, 519, -315, 158, -82, 27, -13, 2, -1}, {1, 9, 49, 189, 651, 2138, 6847, 21805, 69781, 225260, 734119, 2413746, 7995417, 26639534, 89150537, 299309821, 1007213417, 3394930835}, 20] (* Eric W. Weisstein, Oct 01 2025 *)
CoefficientList[Series[(1 - 4 x + 4 x^2 - 29 x^3 + 150 x^4 - 334 x^5 + 507 x^6 - 525 x^7 + 296 x^8 - 153 x^9 - 11 x^10 + 26 x^11 - 58 x^12 + 9 x^13 - 16 x^14 + 2 x^15 - x^16)/((-1 + 2 x + x^3)^2 (-1 + 2 x - x^2 + x^3)^3 (-1 + 3 x + x^2 + x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Oct 01 2025 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 25 2024
EXTENSIONS
a(1)-a(2) and a(8) onwards from Andrew Howroyd, May 29 2025
STATUS
approved