OFFSET
0,4
COMMENTS
This is a rescaled version of the number of spanning trees in the cube of an n-cycle. See A331905 for details. - N. J. A. Sloane, Feb 06 2020
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000 [Jul 09 2015; a(0) inserted by Georg Fischer, Jan 27 2020]
G. Baron et al., The number of spanning trees in the square of a cycle, Fib. Quart., 23 (1985), 258-264.
Tsuyoshi Miezaki, A note on spanning trees.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.
Index entries for linear recurrences with constant coefficients, signature (0,4,0,1,0,4,0,-1).
MAPLE
A005822:=-z*(z-1)*(1+z)*(z**4+z**3-z**2+z+1)/(-4*z**6-z**4-4*z**2+1+z**8); # [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation; adapted to offset 0 by Georg Fischer, Jan 27 2020]
MATHEMATICA
CoefficientList[Series[x (1 - x^2) (x^4 + x^3 - x^2 + x + 1) / (x^8 - 4 x^6 - x^4 - 4 x^2 + 1), {x, 0, 35}], x] (* Vincenzo Librandi, Jan 28 2020 *)
PROG
(PARI) Vec(-x*(x-1)*(x+1)*(x^4+x^3-x^2+x+1)/(x^8-4*x^6-x^4-4*x^2+1) + O(x^50)) \\ Colin Barker, Jul 09 2015
(MAGMA) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); [0] cat Coefficients(R!( x*(1-x^2)*(x^4+x^3-x^2+x+1) / (x^8-4*x^6-x^4-4*x^2+1))); // Vincenzo Librandi, Jan 28 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
G.f. adapted to the offset from Colin Barker, Jul 09 2015
Entry revised by N. J. A. Sloane, Jan 25 2020 and Feb 06 2020.
STATUS
approved