OFFSET
0,2
COMMENTS
The n-helm graph is defined for n >= 3. The sequence has been extrapolated to n = 0 using the recurrence. - Andrew Howroyd, Jan 26 2023
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
Eric Weisstein's World of Mathematics, Edge Cut
Eric Weisstein's World of Mathematics, Helm Graph
Index entries for linear recurrences with constant coefficients, signature (13,-46,50,-16).
FORMULA
G.f.: (1 - 7*x + 22*x^2 - 2*x^3)/((1 - x)*(1 - 8*x)*(1 - 4*x + 2*x^2)). - Andrew Howroyd, Jan 26 2023
a(n) = 2 + 8^n - (2 - sqrt(2))^n - (2 + sqrt(2))^n. - Eric W. Weisstein, Mar 07 2023
MATHEMATICA
Table[2 + 8^n - (2 - Sqrt[2])^n - (2 + Sqrt[2])^n, {n, 0, 20}] // Expand (* Eric W. Weisstein, Mar 07 2023 *)
LinearRecurrence[{13, -46, 50, -16}, {1, 6, 54, 474}, 20] (* Eric W. Weisstein, Mar 07 2023 *)
CoefficientList[Series[-((-1 + 7 x - 22 x^2 + 2 x^3)/((-1 + x) (-1 + 8 x) (1 - 4 x + 2 x^2))), {x, 0, 20}], x] (* Eric W. Weisstein, Mar 07 2023 *)
PROG
(PARI) Vec((1 - 7*x + 22*x^2 - 2*x^3)/((1 - x)*(1 - 8*x)*(1 - 4*x + 2*x^2)) + O(x^21)) \\ Andrew Howroyd, Jan 26 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 30 2022
EXTENSIONS
a(0)-a(2) prepended and terms a(10) and beyond from Andrew Howroyd, Jan 26 2023
STATUS
approved