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 A162147 #38 Apr 01 2021 01:43:35
%S A162147 0,3,14,38,80,145,238,364,528,735,990,1298,1664,2093,2590,3160,3808,
%T A162147 4539,5358,6270,7280,8393,9614,10948,12400,13975,15678,17514,19488,
%U A162147 21605,23870,26288,28864,31603,34510,37590,40848,44289,47918,51740,55760
%N A162147 a(n) = n*(n+1)*(5*n + 4)/6.
%C A162147 Partial sums of A005475.
%C A162147 Suppose we extend the triangle in A215631 to a symmetric array by reflection about the main diagonal. The array is defined by m(i,j) = i^2 + i*j + j^2: 3, 7, 13, ...; 7, 12, 19, ...; 13, 19, 27, .... Then a(n) is the sum of the n-th antidiagonal. Examples: 3, 7 + 7, 13 + 12 + 13, 21 + 19 + 19 + 21, etc. - _J. M. Bergot_, Jun 25 2013
%C A162147 Binomial transform of [0,3,8,5,0,0,0,...]. - _Alois P. Heinz_, Mar 10 2015
%H A162147 Jinyuan Wang, <a href="/A162147/b162147.txt">Table of n, a(n) for n = 0..1000</a>
%H A162147 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A162147 From _R. J. Mathar_, Jun 27 2009: (Start)
%F A162147 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4)
%F A162147 a(n) = A033994(n) + A000217(n).
%F A162147 G.f.: x*(3+2*x)/(1-x)^4. (End)
%F A162147 a(n) = A035005(n+1)/4. - _Johannes W. Meijer_, Feb 04 2010
%F A162147 a(n) = Sum_{i=0..n} i*(n + 1 + i). - _Bruno Berselli_, Mar 17 2016
%F A162147 E.g.f.: x*(18 + 24*x + 5*x^2)*exp(x)/6. - _G. C. Greubel_, Apr 01 2021
%e A162147 For n=4, a(4) = 0*(5+0) + 1*(5+1) + 2*(5+2) + 3*(5+3) + 4*(5+4) = 80. - _Bruno Berselli_, Mar 17 2016
%p A162147 A162147:= n-> n*(n+1)*(5*n+4)/6; seq(A162147(n), n=0..40); # _G. C. Greubel_, Apr 01 2021
%t A162147 Table[(n(n+1)(5n+4))/6,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,3,14,38},50] (* _Harvey P. Dale_, May 04 2013 *)
%o A162147 (PARI) a(n)=n*(n+1)*(5*n+4)/6 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A162147 (Magma) [n*(n+1)*(5*n+4)/6: n in [0..40]]; // _G. C. Greubel_, Apr 01 2021
%o A162147 (Sage) [n*(n+1)*(5*n+4)/6 for n in (0..40)] # _G. C. Greubel_, Apr 01 2021
%Y A162147 Cf. A002412, A002413, A006331, A016061, A033994.
%K A162147 nonn,easy
%O A162147 0,2
%A A162147 _Vladimir Joseph Stephan Orlovsky_, Jun 25 2009
%E A162147 Definition rephrased by _R. J. Mathar_, Jun 27 2009