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 A236267 #35 Oct 19 2024 15:44:33
%S A236267 1,12,39,82,141,216,307,414,537,676,831,1002,1189,1392,1611,1846,2097,
%T A236267 2364,2647,2946,3261,3592,3939,4302,4681,5076,5487,5914,6357,6816,
%U A236267 7291,7782,8289,8812,9351,9906,10477,11064,11667,12286,12921,13572,14239,14922,15621,16336
%N A236267 a(n) = 8*n^2 + 3*n + 1.
%C A236267 Positions a(n) of hexagonal numbers such that h(a(n)) = h(a(n)-1) + h(4*n+1), where h = A000384.
%C A236267 First bisection of A057029. The sequence contains infinitely many squares: 1, 676, 779689, 899760016, ... [_Bruno Berselli_, Jan 24 2014]
%H A236267 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A236267 From _Colin Barker_, Jan 21 2014: (Start)
%F A236267 G.f.: -(6*x^2 + 9*x + 1)/(x-1)^3.
%F A236267 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A236267 E.g.f.: exp(x)*(1 + 11*x + 8*x^2). - _Elmo R. Oliveira_, Oct 19 2024
%e A236267 For n=5, A000384(a(5)) = 93096 = A000384(a(5)-1) + A000384(4*5+1) = 92235 + 861.
%t A236267 Table[8 n^2 + 3 n + 1, {n, 0, 50}] (* _Bruno Berselli_, Jan 24 2014 *)
%t A236267 LinearRecurrence[{3,-3,1},{1,12,39},50] (* _Harvey P. Dale_, May 26 2019 *)
%o A236267 (PARI) Vec(-(6*x^2+9*x+1)/(x-1)^3 + O(x^100)) \\ _Colin Barker_, Jan 21 2014
%o A236267 (Magma) [8*n^2+3*n+1: n in [0..50]]; // _Bruno Berselli_, Jan 24 2014
%Y A236267 Cf. A000384, A057029, A064225, A152948, A236257.
%K A236267 nonn,easy
%O A236267 0,2
%A A236267 _Vladimir Shevelev_, Jan 21 2014
%E A236267 More terms from _Colin Barker_, Jan 21 2014
%E A236267 a(44)-a(45) from _Elmo R. Oliveira_, Oct 19 2024