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.
%I A008722 #33 Jun 20 2025 17:23:42
%S A008722 1,0,2,0,3,0,4,0,5,1,6,2,7,3,8,4,9,5,11,6,13,7,15,8,17,9,19,11,21,13,
%T A008722 23,15,25,17,27,19,30,21,33,23,36,25,39,27,42,30,45,33,48,36,51,39,54,
%U A008722 42,58,45,62,48,66,51,70,54,74,58,78,62,82,66,86,70,90,74,95,78,100,82
%N A008722 Molien series for 3-dimensional group [2,9] = *229.
%C A008722 It appears that a(n) is the number of (n+11)-digit fixed points under the base-7 Kaprekar map A165071 (see A165075 for the list of fixed points). - _Joseph Myers_, Sep 04 2009
%C A008722 a(n) is the number of partitions of n into parts 2 and 9 where there are two kinds of parts 2. - _Hoang Xuan Thanh_, Jun 20 2025
%H A008722 G. C. Greubel, <a href="/A008722/b008722.txt">Table of n, a(n) for n = 0..1000</a>
%H A008722 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=225">Encyclopedia of Combinatorial Structures 225</a>
%H A008722 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H A008722 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1,0,0,0,0,1,0,-2,0,1).
%F A008722 G.f.: 1/((1-x^2)^2*(1-x^9)).
%F A008722 a(n) = 2*a(n-2) - a(n-4) + a(n-9) - 2*a(n-11) + a(n-13). - _R. J. Mathar_, Dec 18 2014
%F A008722 a(n) = floor((n^2 + n*(13+9*(-1)^n) + 62*(-1)^n + 75)/72) - [(n mod 9)=7], where [] is Iverson bracket. - _Hoang Xuan Thanh_, Jun 20 2025
%p A008722 1/((1-x^2)^2*(1-x^9)); seq(coeff(series(%, x, n+1), x, n), n = 0..80); # modified by _G. C. Greubel_, Sep 09 2019
%t A008722 LinearRecurrence[{0,2,0,-1,0,0,0,0,1,0,-2,0,1}, {1,0,2,0,3,0,4,0,5,1,6, 2,7}, 80] (* _Ray Chandler_, Jul 15 2015 *)
%o A008722 (PARI) my(x='x+O('x^80)); Vec(1/((1-x^2)^2*(1-x^9))) \\ _G. C. Greubel_, Sep 09 2019
%o A008722 (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^2)^2*(1-x^9)) )); // _G. C. Greubel_, Sep 09 2019
%o A008722 (Sage)
%o A008722 def A008722_list(prec):
%o A008722 P.<x> = PowerSeriesRing(ZZ, prec)
%o A008722 return P( 1/((1-x^2)^2*(1-x^9)) ).list()
%o A008722 A008722_list(80) # _G. C. Greubel_, Sep 09 2019
%o A008722 (GAP) a:=[1,0,2,0,3,0,4,0,5,1,6,2,7];; for n in [14..80] do a[n]:= 2*a[n-2] -a[n-4]+a[n-9]-2*a[n-11]+a[n-13]; od; a; # _G. C. Greubel_, Sep 09 2019
%K A008722 nonn,easy
%O A008722 0,3
%A A008722 _N. J. A. Sloane_