OFFSET
1,1
COMMENTS
Sequence extrapolated to n=1 and n=2 using the recurrence. - Andrew Howroyd, Jan 11 2018
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Eulerian Cycle
Index entries for linear recurrences with constant coefficients, signature (13, -48, 52, -16).
FORMULA
From Andrew Howroyd, Jan 11 2018: (Start)
a(n) = 13*a(n-1) - 48*a(n-2) + 52*a(n-3) - 16*a(n-4).
G.f.: 4*x*(1 - 2*x - 2*x^2)/((1 - 8*x + 4*x^2)*(1 - 4*x)*(1 - x)).
(End)
From Eric W. Weisstein, Jan 12 2018: (Start)
a(n) = 2^n*((2 - sqrt(3))^n + (2 + sqrt(3))^n) - 2/3*(2 + 4^n).
a(n) = 2^n*A003500(n) - 2/3*(2 + 4^n).
(End)
MATHEMATICA
Table[2^n ((2 - Sqrt[3])^n + (2 + Sqrt[3])^n) - 2/3 (2 + 4^n), {n, 20}] // Expand
Table[2^n LucasL[2 n, Sqrt[2]] - 2/3 (2 + 4^n), {n, 20}] // Round
LinearRecurrence[{13, -48, 52, -16}, {4, 44, 372, 2932}, 20]
CoefficientList[Series[-4 (-1 + 2 x + 2 x^2)/(1 - 13 x + 48 x^2 - 52 x^3 + 16 x^4), {x, 0, 20}], x]
PROG
(PARI) Vec(4*(1 - 2*x - 2*x^2)/((1 - 8*x + 4*x^2)*(1 - 4*x)*(1 - x)) + O(x^30)) \\ Andrew Howroyd, Jan 11 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 29 2017
STATUS
approved