cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A025765 Expansion of 1/((1-x)(1-x^2)(1-x^9)).

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%I A025765 #11 Aug 14 2021 14:09:59
%S A025765 1,1,2,2,3,3,4,4,5,6,7,8,9,10,11,12,13,14,16,17,19,20,22,23,25,26,28,
%T A025765 30,32,34,36,38,40,42,44,46,49,51,54,56,59,61,64,66,69,72,75,78,81,84,
%U A025765 87,90,93,96,100,103,107,110
%N A025765 Expansion of 1/((1-x)(1-x^2)(1-x^9)).
%H A025765 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,0,0,0,1,-1,-1,1).
%F A025765 a(n)= +a(n-1) +a(n-2) -a(n-3) +a(n-9) -a(n-10) -a(n-11) +a(n-12). - _R. J. Mathar_, Mar 22 2011
%p A025765 A014018 := proc(n) if n < 0 then 0; else coeftayl(1/(1+x^3+x^6),x=0,n) ; end if; end proc:
%p A025765 A061347 := proc(n) op(1+(n mod 3),[1,1,-2]) ; end proc:
%p A025765 A025765 := proc(n) 1/3*n +173/216 +1/36*n^2 +1/8*(-1)^n + ( A014018(n-2)+A014018(n-4)+A014018(n-5))/3 - A061347(n+2)/27 ; end proc:
%p A025765 seq(A025765(n),n=0..40) ; # _R. J. Mathar_, Mar 22 2011
%t A025765 CoefficientList[Series[1/((1-x)(1-x^2)(1-x^9)),{x,0,60}],x] (* or *) LinearRecurrence[{1,1,-1,0,0,0,0,0,1,-1,-1,1},{1,1,2,2,3,3,4,4,5,6,7,8},60] (* _Harvey P. Dale_, Aug 14 2021 *)
%o A025765 (PARI) Vec(1/((1-x)*(1-x^2)*(1-x^9))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%K A025765 nonn,easy
%O A025765 0,3
%A A025765 _N. J. A. Sloane_