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 A264938 #61 Sep 08 2022 08:46:14
%S A264938 0,1,6,16,29,46,68,93,122,156,193,234,280,329,382,440,501,566,636,709,
%T A264938 786,868,953,1042,1136,1233,1334,1440,1549,1662,1780,1901,2026,2156,
%U A264938 2289,2426,2568,2713,2862,3016,3173,3334,3500,3669,3842,4020,4201,4386,4576,4769
%N A264938 a(n) = n*(2*n-1) + floor(n/3).
%C A264938 Sequence extended to the left:
%C A264938 ..., 133, 102, 76, 53, 34, 20, 9, 2, 0, 1, 6, 16, 29, 46, 68, 93, ...
%C A264938 Conjecture: after 0, a(n) provides the first bisection of A264041.
%C A264938 Conjecture: 2, 9, 20, 34, 53, 76, 102, 133, ... is A248121.
%H A264938 Colin Barker, <a href="/A264938/b264938.txt">Table of n, a(n) for n = 0..1000</a>
%H A264938 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H A264938 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F A264938 a(n) = a(n-3) + 12*n - 20 for n>2.
%F A264938 From _Colin Barker_, Dec 02 2015: (Start)
%F A264938 a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>4.
%F A264938 G.f.: x*(1+x)^2*(1+2*x) / ((1-x)^3*(1+x+x^2)).
%F A264938 (End)
%F A264938 a(n) = A000217(2n-1) + A002264(n).
%F A264938 a(n) + a(-n) = 3*A256320(n).
%F A264938 a(n +8) - a(n -7) = 20*A016777(n).
%F A264938 a(n+16) - a(n-14) = 20*A016969(n).
%F A264938 a(n+23) - a(n-22) = 20*A017197(n).
%F A264938 a(n+31) - a(n-29) = 20*A017641(n).
%F A264938 Generalization of the previous four formulas:
%F A264938 a(n+30*k +8) - a(n-30*k -7) = 20*(4*k+1)*(3*n+1).
%F A264938 a(n+30*k+16) - a(n-30*k-14) = 20*(2*k+1)*(6*n+5).
%F A264938 a(n+30*k+24) - a(n-30*k-21) = 20*(4*k+3)*(3*n+4).
%F A264938 a(n+30*k+32) - a(n-30*k-28) = 20*(2*k+2)*(6*n+11).
%F A264938 E.g.f.: (6*x^2+4*x-1)*exp(x)/3 + (cos(sqrt(3)*x/2)/3 +sqrt(3)*sin(sqrt(3)*x/2)/9)*exp(-x/2). - _Robert Israel_, Dec 02 2015
%p A264938 seq(n*(2*n-1) + floor(n/3), n=0..100); # _Robert Israel_, Dec 02 2015
%t A264938 Table[n (2 n - 1) + Floor[n/3], {n, 0, 50}] (* _Vincenzo Librandi_, Dec 02 2015 *)
%t A264938 LinearRecurrence[{2,-1,1,-2,1},{0,1,6,16,29},60] (* _Harvey P. Dale_, Oct 13 2020 *)
%o A264938 (PARI) concat(0, Vec(x*(1+x)^2*(1+2*x)/((1-x)^3*(1+x+x^2)) + O(x^100))) \\ _Colin Barker_, Dec 02 2015
%o A264938 (PARI) a(n) = n*(2*n-1) + n\3; \\ _Altug Alkan_, Dec 01 2015
%o A264938 (Magma) [n*(2*n-1)+Floor(n/3): n in [0..60]]; // _Vincenzo Librandi_, Dec 02 2015
%Y A264938 Second bisection of A260708.
%Y A264938 Cf. A000217, A002264, A016777, A016969, A017197, A017641, A099837, A248121, A256320, A260699, A264041.
%Y A264938 Cf. A171452: A000217(n-1) + A002264(n).
%K A264938 nonn,easy
%O A264938 0,3
%A A264938 _Paul Curtz_, Nov 29 2015
%E A264938 Edited by _Bruno Berselli_, Dec 01 2015