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 A226292 #32 Sep 08 2022 08:46:05
%S A226292 2,6,13,22,34,48,65,84,106,130,157,186,218,252,289,328,370,414,461,
%T A226292 510,562,616,673,732,794,858,925,994,1066,1140,1217,1296,1378,1462,
%U A226292 1549,1638,1730,1824,1921,2020,2122,2226,2333,2442,2554,2668,2785,2904,3026,3150
%N A226292 (10*n^2+4*n+(1-(-1)^n))/8.
%C A226292 The number of binary pattern classes in the (3,n)-rectangular grid with 2 '1's and (n-2) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other, n<10.
%C A226292 Column k=2 of A226290.
%C A226292 For n even, a(n) is A202803; for n odd, a(n) is A190816.
%C A226292 Number of lattice points (x,y) in the region bounded by y < 3x, y > x/2 and x <= n. - _Wesley Ivan Hurt_, Oct 31 2014
%H A226292 Vincenzo Librandi, <a href="/A226292/b226292.txt">Table of n, a(n) for n = 1..1000</a>
%H A226292 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A226292 a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>4, a(1)=2, a(2)=6, a(3)=13, a(4)=22.
%F A226292 a(n) = 2*a(n-2)-a(n-4)+10 for n>4, a(1)=2, a(2)=6, a(3)=13, a(4)=22.
%F A226292 a(n) = a(n-1)+a(n-2)-a(n-3)+5 for n>3, a(1)=2, a(2)=6, a(3)=13.
%F A226292 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3)+(-1)^n for n>3, a(1)=2, a(2)=6, a(3)=13.
%F A226292 a(n) = 2*a(n-1)-a(n-2)+2+(1-(-1)^n)/2 for n>2, a(1)=2, a(2)=6.
%F A226292 G.f.: x*(2+2*x+x^2)/((1+x)*(1-x)^3). - _Bruno Berselli_, Jun 03 2013
%p A226292 A226292:=n->(10*n^2+4*n+(1-(-1)^n))/8: seq(A226292(n), n=1..50); # _Wesley Ivan Hurt_, Oct 31 2014
%t A226292 CoefficientList[Series[(2 + 2 x + x^2) / ((1 + x) (1 - x)^3), {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 04 2013 *)
%t A226292 LinearRecurrence[{2,0,-2,1},{2,6,13,22},60] (* _Harvey P. Dale_, Feb 01 2019 *)
%o A226292 (Magma) [(10*n^2+4*n+(1-(-1)^n))/8: n in [1..50]]; // _Vincenzo Librandi_, Sep 04 2013
%Y A226292 Cf. A190816, A202803, A226290.
%K A226292 nonn,easy
%O A226292 1,1
%A A226292 _Yosu Yurramendi_, Jun 02 2013
%E A226292 More terms from _Vincenzo Librandi_, Sep 04 2013