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 A362652 #27 Jun 26 2023 16:09:49
%S A362652 2,4,7,12,16,24,29,40,46,60,67,84,92,112,121,144,154,180,191,220,232,
%T A362652 264,277,312,326,364,379,420,436,480,497,544,562,612,631,684,704,760,
%U A362652 781,840,862,924,947,1012,1036,1104,1129,1200,1226,1300,1327
%N A362652 Expansion of g.f. x*(-2 - 2*x + x^2 - x^3)/((1 + x)^2 *(-1 + x)^3).
%C A362652 a(n) gives the number of vertices encountered along the shortest walk that encounters every edge at least once on the graph with n vertices where the graph is both complete and every node also has an edge to itself.
%C A362652 a(n) can be thought of as the length of a list made up using n distinct elements where every element is next to every other element (including a copy of itself) at least once. Such a list could be used forwards and backward when kerning a font as a way to minimize the number of characters typed in total.
%H A362652 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A362652 a(n) = n + (n mod 2) + (n * (n - (n mod 2)))/2.
%F A362652 a(2*n) = 2*n + 2*n^2;
%F A362652 a(2*n - 1) = 1 - n + 2*n^2.
%F A362652 E.g.f.: (2 + x)*(exp(x)*x + sinh(x))/2. - _Stefano Spezia_, May 07 2023
%e A362652 G.f.: 2*x + 4*x^2 + 7*x^3 + 12*x^4 + 16*x^5 + 24*x^6 + 29*x^7 + 40*x^8 + 46*x^9 + ...
%t A362652 CoefficientList[Series[x(-2-2x+x^2-x^3)/((1+x)^2(-1+x)^3), {x, 0, 50}], x]
%t A362652 (* or *)
%t A362652 LinearRecurrence[{1, 2, -2, -1, 1}, {2, 4, 7, 12, 16}, 50]
%o A362652 (Python) def a(n: int): return n + (n & 1) + n * ( n >> 1 )
%Y A362652 Cf. A053439.
%K A362652 nonn,easy
%O A362652 1,1
%A A362652 _Jonathon Priestley_, Apr 28 2023