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 A353212 #18 Jun 18 2025 23:19:24
%S A353212 1,1,2,2,3,4,5,6,7,7,8,9,10,10,11,12,13,13,14,15,16,16,17,18,19,19,20,
%T A353212 21,22,22,23,24,25,25,26,27,28,28,29,30,31,31,32,33,34,34,35,36,37,37,
%U A353212 38,39,40,40,41,42,43,43,44,45,46,46,47,48,49,49,50,51,52,52
%N A353212 Hadwiger number of the n-path complement graph.
%C A353212 A contraction in the complement of any set of paths reduces the total number of edges in the complement by at most 4. This gives an upper bound for the Hadwiger number which is obtainable for all path lengths except 4 and 5. In particular, for n >= 6, the complement of a P_n reduces to the complement of a P_{n-4} union 3 universal nodes by contracting the second and second to last nodes of the path. With P_8 and P_9 the 2nd and 6th nodes should be contracted (instead of reducing to P_4 or P_5 respectively). - _Andrew Howroyd_, Jun 18 2025
%H A353212 Andrew Howroyd, <a href="/A353212/b353212.txt">Table of n, a(n) for n = 1..1000</a>
%H A353212 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HadwigerNumber.html">Hadwiger Number</a>.
%H A353212 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PathComplementGraph.html">Path Complement Graph</a>.
%H A353212 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A353212 a(n) = floor((3*n + 1)/4) = A037915(n+1) for n >= 6. - _Andrew Howroyd_, Jun 18 2025
%o A353212 (PARI) a(n) = (3*n + 1)\4 - (n==4||n==5) \\ _Andrew Howroyd_, Jun 18 2025
%Y A353212 Cf. A037915.
%K A353212 nonn,easy
%O A353212 1,3
%A A353212 _Eric W. Weisstein_, Apr 30 2022
%E A353212 a(16) onwards from _Andrew Howroyd_, Jun 18 2025