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 A132127 #17 Sep 07 2025 21:51:32
%S A132127 1,6,17,37,69,116,181,267,377,514,681,881,1117,1392,1709,2071,2481,
%T A132127 2942,3457,4029,4661,5356,6117,6947,7849,8826,9881,11017,12237,13544,
%U A132127 14941,16431,18017,19702,21489,23381,25381,27492,29717,32059,34521,37106,39817,42657,45629
%N A132127 a(n) = (n^3 + 3*n - 2)/2.
%C A132127 Binomial transform of [1, 5, 6, 3, 0, 0, 0, ...].
%C A132127 Sum of the numbers in the top row and 1st column of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows (see example). - _Wesley Ivan Hurt_, May 18 2021
%H A132127 Andrew Howroyd, <a href="/A132127/b132127.txt">Table of n, a(n) for n = 1..1000</a>
%H A132127 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A132127 a(n) = n*(n^2 + 3)/2 - 1.
%F A132127 From _Elmo R. Oliveira_, Sep 07 2025: (Start)
%F A132127 G.f.: x*(1 + 2*x - x^2 + x^3)/(x-1)^4.
%F A132127 E.g.f.: 1 + (x^3 + 3*x^2 + 4*x - 2)*exp(x)/2.
%F A132127 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)
%e A132127 From _Wesley Ivan Hurt_, May 18 2021: (Start)
%e A132127 Sum of the numbers in the top row and 1st column.
%e A132127 [1 2 3 4 5]
%e A132127 [1 2 3 4] [6 7 8 9 10]
%e A132127 [1 2 3] [5 6 7 8] [11 12 13 14 15]
%e A132127 [1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]
%e A132127 [1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]
%e A132127 ------------------------------------------------------------------------
%e A132127 n 1 2 3 4 5
%e A132127 ------------------------------------------------------------------------
%e A132127 a(n) 1 6 17 37 69
%e A132127 ------------------------------------------------------------------------
%e A132127 (End)
%t A132127 Table[n*(n^2 + 3)/2 - 1, {n, 80}] (* _Wesley Ivan Hurt_, May 18 2021 *)
%o A132127 (PARI) a(n) = (n^3 + 3*n - 2)/2; \\ _Andrew Howroyd_, Apr 17 2021
%Y A132127 Row sums of triangle A132119 and A132128.
%K A132127 nonn,easy,changed
%O A132127 1,2
%A A132127 _Gary W. Adamson_, Aug 10 2007
%E A132127 Edited and terms a(13) and beyond from _Andrew Howroyd_, Apr 17 2021