A008770 - OEIS

%I #16 Sep 08 2022 08:44:36

%S 1,1,2,3,5,6,9,11,15,19,24,29,37,44,53,63,75,87,102,117,135,154,175,

%T 197,223,249,278,309,343,378,417,457,501,547,596,647,703,760,821,885,

%U 953,1023,1098,1175,1257,1342,1431,1523,1621,1721,1826,1935,2049,2166,2289,2415,2547,2683

%N Expansion of (1+x^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

%H G. C. Greubel, <a href="/A008770/b008770.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1,-1,1,-1,2,-1).

%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) - a(n-5) + a(n-6) - a(n-7) + 2*a(n-8) - a(n-9); a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=5, a(5)=6, a(6)=9, a(7)=11, a(8)=15. - _Harvey P. Dale_, Oct 02 2012

%p seq(coeff(series((1+x^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)), x, n+1), x, n), n = 0 .. 60); # _G. C. Greubel_, Sep 10 2019

%t CoefficientList[Series[(x^9+1)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4),{x,0,60}],x] (* or *) LinearRecurrence[{2,-1,1,-1,-1,1,-1,2,-1}, {1,1,2,3,5,6,9,11, 15}, 60] (* _Harvey P. Dale_, Oct 02 2012 *)

%o (PARI) my(x='x+O('x^60)); Vec((1+x^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))) \\ _G. C. Greubel_, Sep 10 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // _G. C. Greubel_, Sep 10 2019

%o (Sage)

%o def A008770_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P((1+x^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()

%o A008770_list(60) # _G. C. Greubel_, Sep 10 2019

%o (GAP) a:=[1,1,2,3,5,6,9,11,15];; for n in [10..60] do a[n]:=2*a[n-1]-a[n-2]+a[n-3]-a[n-4]-a[n-5]+a[n-6]-a[n-7]+2*a[n-8]-a[n-9]; od; a; # _G. C. Greubel_, Sep 10 2019

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E Terms a(45) onward added by _G. C. Greubel_, Sep 10 2019