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 A257083 #17 Oct 30 2022 07:11:41
%S A257083 1,2,6,9,17,22,34,41,57,66,86,97,121,134,162,177,209,226,262,281,321,
%T A257083 342,386,409,457,482,534,561,617,646,706,737,801,834,902,937,1009,
%U A257083 1046,1122,1161,1241,1282,1366,1409,1497,1542,1634,1681,1777,1826,1926,1977
%N A257083 Partial sums of A257088.
%C A257083 Equivalently, numbers of the form m*(3*m+2)+1, where m = 0, -1, 1, -2, 2, -3, 3, ... - _Bruno Berselli_, Jan 05 2016
%C A257083 Also, numbers k such that 3*k-2 is a square. - _Bruno Berselli_, Jan 30 2018
%H A257083 Reinhard Zumkeller, <a href="/A257083/b257083.txt">Table of n, a(n) for n = 0..10000</a>
%H A257083 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A257083 From _Bruno Berselli_, Jan 05 2016: (Start)
%F A257083 G.f.: (1 + x + 2*x^2 + x^3 + x^4)/((1 + x)^2*(1 - x)^3).
%F A257083 a(n) = (6*n*(n+1) + (2*n+1)*(-1)^n + 7)/8. (End)
%F A257083 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). - _Wesley Ivan Hurt_, Oct 30 2022
%t A257083 Table[(6 n (n + 1) + (2 n + 1) (-1)^n + 7)/8, {n, 0, 60}] (* _Bruno Berselli_, Jan 05 2016 *)
%o A257083 (Haskell)
%o A257083 a257083 n = a257083_list !! n
%o A257083 a257083_list = scanl1 (+) a257088_list
%o A257083 (PARI) vector(60, n, n--; (6*n*(n+1)+(2*n+1)*(-1)^n+7)/8) \\ _Bruno Berselli_, Jan 05 2016
%o A257083 (Magma) [(6*n*(n+1) + (2*n+1)*(-1)^n + 7)/8 : n in [0..60]]; // _Wesley Ivan Hurt_, Oct 30 2022
%Y A257083 Cf. A246695 (partial sums), A257088.
%Y A257083 Cf. A056109: numbers of the form m*(3*m+2)+1 for nonnegative m.
%K A257083 nonn,easy
%O A257083 0,2
%A A257083 _Reinhard Zumkeller_, Apr 17 2015