OFFSET
1,1
COMMENTS
The n-flower graph can be defined without using parallel edges for n >= 3. It is a snark for odd n >= 5. The sequence has been extended to n=1 using the recurrence. - Andrew Howroyd, May 24 2025
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Flower Snark.
Eric Weisstein's World of Mathematics, Graph Cycle.
Index entries for linear recurrences with constant coefficients, signature (11,-40,32,125,-295,205,-47,40,-32,-125,295,-204,36).
FORMULA
G.f.: x*(4 - 29*x + 95*x^2 - 259*x^3 + 405*x^4 + 162*x^5 - 1114*x^6 + 1385*x^7 - 1475*x^8 + 625*x^9 + 177*x^10 - 264*x^11 + 72*x^12)/((1 - x)^2*(1 + x)*(1 - 2*x)*(1 + 2*x)*(1 - 3*x)^2*(1 - 4*x + x^2)*(1 - x + x^2)*(1 + x + x^2)).
MATHEMATICA
Table[1/2 (-5 - 2 (-1)^n - 2^n (1 + (-1)^n) - 3 n + 3^n (n + 1) + 4 ChebyshevT[n, -1/2] + 4 ChebyshevT[n, 1/2] + 4 ChebyshevT[n, 2]), {n, 20}] (* Eric W. Weisstein, Aug 28 2025 *)
LinearRecurrence[{11, -40, 32, 125, -295, 205, -47, 40, -32, -125, 295, -204, 36}, {4, 15, 100, 369, 1444, 5181, 18820, 66885, 238852, 847899, 3019108, 10751055, 38407204}, 20] (* Eric W. Weisstein, Aug 28 2025 *)
CoefficientList[Series[(4 - 29 x + 95 x^2 - 259 x^3 + 405 x^4 + 162 x^5 - 1114 x^6 + 1385 x^7 - 1475 x^8 + 625 x^9 + 177 x^10 - 264 x^11 + 72 x^12)/((1 - x)^2 (1 + x) (1 - 2 x) (1 + 2 x) (1 - 3 x)^2 (1 - 4 x + x^2) (1 - x + x^2) (1 + x + x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 28 2025 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 16 2023
EXTENSIONS
a(1)-a(4) and a(17) onwards from Andrew Howroyd, May 24 2025
STATUS
approved