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 A193867 #28 May 11 2025 01:08:51
%S A193867 1,7,11,29,37,67,79,121,137,191,211,277,301,379,407,497,529,631,667,
%T A193867 781,821,947,991,1129,1177,1327,1379,1541,1597,1771,1831,2017,2081,
%U A193867 2279,2347,2557,2629,2851,2927,3161,3241,3487,3571,3829,3917,4187,4279
%N A193867 Odd central polygonal numbers.
%C A193867 Even triangular numbers plus 1.
%C A193867 Union of A188135 and A185438 without repetitions (A188135 is a bisection of this sequence. Another bisection is A185438 but without its initial term).
%H A193867 Colin Barker, <a href="/A193867/b193867.txt">Table of n, a(n) for n = 1..1000</a>
%H A193867 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A193867 a(n) = A000124(A014601(n-1)).
%F A193867 a(n) = 1 + A014494(n-1).
%F A193867 G.f.: -x*(x^2+1)*(x^2+6*x+1) / ( (1+x)^2*(x-1)^3 ). - _R. J. Mathar_, Aug 25 2011
%F A193867 From _Colin Barker_, Jan 27 2016: (Start)
%F A193867 a(n) = (4*n^2+2*(-1)^n*n-4*n-(-1)^n+3)/2.
%F A193867 a(n) = 2*n^2-n+1 for n even.
%F A193867 a(n) = 2*n^2-3*n+2 for n odd. (End)
%F A193867 Sum_{n>=1} 1/a(n) = 2*Pi*sinh(sqrt(7)*Pi/4)/(sqrt(7)*(2*cosh(sqrt(7)*Pi/4) - sqrt(2))). - _Amiram Eldar_, May 11 2025
%t A193867 Select[Accumulate[Range[0,100]],EvenQ]+1 (* or *) LinearRecurrence[{1,2,-2,-1,1},{1,7,11,29,37},50] (* _Harvey P. Dale_, Nov 29 2014 *)
%o A193867 (PARI) Vec(-x*(x^2+1)*(x^2+6*x+1) / ((1+x)^2*(x-1)^3) + O(x^100)) \\ _Colin Barker_, Jan 27 2016
%Y A193867 Cf. A000124, A014494, A014601, A185438, A188135, A193868.
%K A193867 nonn,easy
%O A193867 1,2
%A A193867 _Omar E. Pol_, Aug 15 2011