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 A236453 #20 Oct 11 2024 11:39:20
%S A236453 1,3,4,8,11,17,22,30,37,47,56,68,79,93,106,122,137,155,172,192,211,
%T A236453 233,254,278,301,327,352,380,407,437,466,498,529,563,596,632,667,705,
%U A236453 742,782,821,863,904,948,991,1037,1082,1130,1177,1227,1276,1328,1379,1433,1486,1542
%N A236453 Number of length n strings on the alphabet {0,1,2} of the form 0^i 1^j 2^k such that i,j,k>=0 and if i=1 then j=k.
%C A236453 The language of all such strings is an example of a language that satisfies the conditions of the pumping lemma for regular languages but is not regular.
%D A236453 Michael Sipser, Introduction to the Theory of Computation, PWS Publishing Co., 1997, page 89.
%H A236453 Andrew Howroyd, <a href="/A236453/b236453.txt">Table of n, a(n) for n = 0..1000</a>
%H A236453 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -2, 1).
%F A236453 G.f.: (1 + x - 2*x^2 + 2*x^3)/((1 - x)^3*(1 + x)).
%F A236453 For even n a(n) = A000124(n).
%F A236453 For odd n a(n) = A000124(n) + 1.
%F A236453 a(n) = (n^2 + n + 3 - (-1)^n)/2. - _Giovanni Resta_, Jan 26 2014
%e A236453 a(3)=8 because we have: 000, 001, 002, 012, 111, 112, 122, 222.
%t A236453 nn=40;a=1/(1-x);CoefficientList[Series[(a-x)a^2+x/(1-x^2),{x,0,nn}],x]
%t A236453 Table[(3 - (-1)^n + n + n^2)/2,{n,0,50}] (* _Giovanni Resta_, Jan 26 2014 *)
%t A236453 LinearRecurrence[{2, 0, -2, 1}, {1, 3, 4, 8}, 50] (* _Hugo Pfoertner_, Oct 10 2024 *)
%o A236453 (PARI) a(n) = (n^2 + n + 3 - (-1)^n)/2 \\ _Charles R Greathouse IV_, Apr 18 2020
%Y A236453 Cf. A000124.
%K A236453 nonn,easy
%O A236453 0,2
%A A236453 _Geoffrey Critzer_, Jan 26 2014
%E A236453 Terms a(41) and beyond from _Andrew Howroyd_, Mar 27 2020