OFFSET
0,2
COMMENTS
Number of 0..n arrays of 7 elements with zero second differences. - R. H. Hardin, Nov 16 2011
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,1,-2,1).
FORMULA
G.f.: (1+x^6)/((1-x)^2*(1-x^6)).
a(n) = 2*a(n-1) -a(n-2) +a(n-6) -2*a(n-7) +a(n-8). - R. H. Hardin, Nov 16 2011
MAPLE
seq(coeff(series((1+x^6)/((1-x)^2*(1-x^6)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 12 2019
MATHEMATICA
CoefficientList[Series[(1+x^6)/(1-x)^2/(1-x^6), {x, 0, 70}], x] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 6, 9, 12}, 70] (* Harvey P. Dale, Oct 13 2012 *)
PROG
(PARI) Vec((1+x^6)/((1-x)^2*(1-x^6)) +O(x^70)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^6)/((1-x)^2*(1-x^6)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008813_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^6)/((1-x)^2*(1-x^6))).list()
A008813_list(70) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 2, 3, 4, 5, 6, 9, 12];; for n in [9..70] do a[n]:=2*a[n-1]-a[n-2] +a[n-6]-2*a[n-7]+a[n-8]; od; a; # G. C. Greubel, Sep 12 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms added by G. C. Greubel, Sep 12 2019
STATUS
approved