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 A127736 #48 Sep 01 2024 14:06:52
%S A127736 1,7,21,46,85,141,217,316,441,595,781,1002,1261,1561,1905,2296,2737,
%T A127736 3231,3781,4390,5061,5797,6601,7476,8425,9451,10557,11746,13021,14385,
%U A127736 15841,17392,19041,20791,22645,24606,26677,28861,31161,33580,36121,38787,41581
%N A127736 a(n) = n*(n^2 + 2*n - 1)/2.
%C A127736 Row sums of A127735.
%C A127736 Row sums of A162610. - _Reinhard Zumkeller_, Jan 19 2013
%C A127736 For n > 0, a(n) is the number of compositions of n+10 into n parts avoiding parts 2 and 3. - _Milan Janjic_, Jan 07 2016
%C A127736 Sum of the numbers in the top row and last 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 A127736 Vincenzo Librandi, <a href="/A127736/b127736.txt">Table of n, a(n) for n = 1..1000</a>
%H A127736 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A127736 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A127736 Row sums of triangle A131416. Also, binomial transform of [1, 6, 8, 3, 0, 0, 0, ...). - _Gary W. Adamson_, Oct 23 2007
%F A127736 a(n) = (n+1)*A000217(n) - n = A006002(n) - n. - _R. J. Mathar_, Jul 21 2009
%F A127736 From _Colin Barker_, Mar 12 2014: (Start)
%F A127736 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A127736 G.f.: -x*(x^2-3*x-1) / (x-1)^4. (End)
%F A127736 a(n) = A057145(n+5,n). - _R. J. Mathar_, Jul 28 2016
%e A127736 From _Wesley Ivan Hurt_, May 18 2021: (Start)
%e A127736 Add all the numbers in the top row and last column.
%e A127736 [1 2 3 4 5]
%e A127736 [1 2 3 4] [6 7 8 9 10]
%e A127736 [1 2 3] [5 6 7 8] [11 12 13 14 15]
%e A127736 [1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]
%e A127736 [1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]
%e A127736 ------------------------------------------------------------------------
%e A127736 n 1 2 3 4 5
%e A127736 ------------------------------------------------------------------------
%e A127736 a(n) 1 7 21 46 85
%e A127736 ------------------------------------------------------------------------
%e A127736 (End)
%p A127736 A127736:=n->n*(n^2+2*n-1)/2; seq(A127736(n), n=1..40); # _Wesley Ivan Hurt_, Mar 14 2014
%t A127736 Table[n*(n^2 + 2*n - 1)/2, {n, 60}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 24 2011 *)
%t A127736 CoefficientList[Series[-(x^2 - 3 x - 1)/(x - 1)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 14 2014 *)
%t A127736 LinearRecurrence[{4,-6,4,-1},{1,7,21,46},60] (* _Harvey P. Dale_, Apr 22 2014 *)
%o A127736 (PARI) Vec(-x*(x^2-3*x-1)/(x-1)^4 + O(x^100)) \\ _Colin Barker_, Mar 12 2014
%o A127736 (PARI) a(n) = n*(n^2+2*n-1)/2; \\ _Altug Alkan_, Jan 07 2016
%Y A127736 Cf. A002260, A127701, A127735, A131416.
%K A127736 nonn,easy
%O A127736 1,2
%A A127736 _Gary W. Adamson_, Jan 26 2007
%E A127736 More terms and new name from _R. J. Mathar_, Jul 21 2009