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 A091573 #24 Jan 30 2018 18:57:36
%S A091573 7,12,17,24,31,36,41,48,55,60,65,72,79,84,89,96,103,108,113,120,127,
%T A091573 132,137,144,151,156,161,168,175,180,185,192,199,204,209,216,223,228,
%U A091573 233,240,247,252,257,264,271,276,281,288,295,300,305,312,319,324,329
%N A091573 Poincaré series [or Poincare series] of the preprojective algebra of an extended Dynkin diagram of type E_6.
%D A091573 I. Reiten, Dynkin diagrams and the representation theory of algebras, Notices of the AMS, Vol. 44, Number 5.
%H A091573 Colin Barker, <a href="/A091573/b091573.txt">Table of n, a(n) for n = 0..1000</a>
%H A091573 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%F A091573 a(n) = 6*n+6 (n odd), 6*n+7 (n==0 (mod 4)), 6*n+5 (n==2 (mod 4)).
%F A091573 G.f.: (7-2*x+7*x^2) / ((1+x^2)*(1-x)^2).
%F A091573 From _Colin Barker_, Oct 18 2015: (Start)
%F A091573 a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>3.
%F A091573 a(n) = (12+(-i)^n+i^n+12*n)/2 where i = sqrt(-1).
%F A091573 (End)
%t A091573 CoefficientList[ Series[ (7 - 2x + 7x^2) / (1 - 2x + 2x^2 - 2x^3 + x^4), {x, 0, 49}], x] (* _Jean-François Alcover_, Dec 02 2011 *)
%o A091573 (PARI) a(n) = (12+(-I)^n+I^n+12*n)/2 \\ _Colin Barker_, Oct 18 2015
%o A091573 (PARI) Vec((7-2*x+7*x^2)/((1+x^2)*(1-x)^2) + O(x^100)) \\ _Colin Barker_, Oct 18 2015
%o A091573 (PARI) a(n) = if(n%2 == 1, 6*n+6, if(n%4 == 0, 6*n+7, 6*n+5));
%o A091573 vector(100, n, a(n-1)) \\ _Altug Alkan_, Oct 18 2015
%Y A091573 Cf. A004525, A091571, A091572, A091574, A091575, A091576, A091577.
%K A091573 easy,nonn
%O A091573 0,1
%A A091573 _Paul Boddington_, Jan 22 2004
%E A091573 G.f. corrected by _Colin Barker_, Oct 18 2015