OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
Svenja Huntemann, Neil A. McKay, Counting Domineering Positions, arXiv:1909.12419 [math.CO], 2019.
Eric Weisstein's World of Mathematics, Ladder Graph
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
Index entries for linear recurrences with constant coefficients, signature (2,0,0,1,1).
FORMULA
a(n) = 2*a(n-1) + a(n-4) + a(n-5) for n>5.
G.f.: x*(1+x^2+x^3+x^4)/((1-x+x^2)*(1-x-2*x^2-x^3)).
MAPLE
seq(coeff(series(x*(1+x^2+x^3+x^4)/(1-2*x-x^4-x^5), x, n+1), x, n), n = 1..35); # G. C. Greubel, Dec 30 2019
MATHEMATICA
Table[3Cos[nPi/3]/13 - 5Sin[nPi/3]/(13 Sqrt[3]) + RootSum[-1 -2# -#^2 +#^3 &, (-6 -72# +80#^2) #^n &]/403, {n, 35}] (* Eric W. Weisstein, Jul 13 2017 *)
LinearRecurrence[{2, 0, 0, 1, 1}, {1, 2, 5, 11, 24}, 35] (* Eric W. Weisstein, Jul 13 2017 *)
CoefficientList[Series[(1+x^2+x^3+x^4)/(1-2x-x^4-x^5), {x, 0, 35}], x] (* Eric W. Weisstein, Jul 13 2017 *)
PROG
(PARI) Vec((1+x^2+x^3+x^4)/((1-x+x^2)*(1-x-2*x^2-x^3)) + O(x^35))
(Magma) R<x>:=PowerSeriesRing(Integers(), 35); Coefficients(R!( x*(1+x^2+x^3+x^4)/(1-2*x-x^4-x^5) )); // G. C. Greubel, Dec 30 2019
(Sage)
def A286945_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1+x^2+x^3+x^4)/(1-2*x-x^4-x^5) ).list()
a=A286945_list(35); a[1:] # G. C. Greubel, Dec 30 2019
(GAP) a:=[1, 2, 5, 11, 24];; for n in [6..35] do a[n]:=2*a[n-1]+a[n-4]+a[n-5]; od; a; # G. C. Greubel, Dec 30 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, May 16 2017
STATUS
approved