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 A264443 #12 Sep 08 2022 08:46:14
%S A264443 0,11,28,52,84,125,176,238,312,399,500,616,748,897,1064,1250,1456,
%T A264443 1683,1932,2204,2500,2821,3168,3542,3944,4375,4836,5328,5852,6409,
%U A264443 7000,7626,8288,8987,9724,10500,11316,12173,13072,14014,15000
%N A264443 a(n) = n*(n + 5)*(n + 10)/6.
%C A264443 It is well-known, and easy to prove, that the product of 3 consecutive integers n*(n + 1)*(n + 2) is divisible by 6. It can be shown that the product of 3 integers in arithmetic progression n*(n + r)*(n + 2*r) is divisible by 6 if and only if r is not divisible by 2 or 3 (see A007310 for these numbers). This is the case r = 5.
%H A264443 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A264443 O.g.f.: x*(6*x^2 - 16*x + 11)/(1 - x)^4.
%F A264443 a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3. - _Vincenzo Librandi_, Nov 16 2015
%p A264443 seq( n*(n + 5)*(n + 10)/6, n = 1..40 );
%t A264443 Table[n (n + 5) (n + 10)/6, {n, 0, 40}] (* _Vincenzo Librandi_, Nov 16 2015 *)
%o A264443 (PARI) vector(100, n, n--; n*(n+5)*(n+10)/6) \\ _Altug Alkan_, Nov 15 2015
%o A264443 (Magma) [n*(n+5)*(n+10)/6: n in [0..40]]; // _Vincenzo Librandi_, Nov 16 2015
%Y A264443 Cf. A007310, A264444, A264445, A264446, A264447, A264448, A264449, A264450.
%K A264443 nonn,easy
%O A264443 0,2
%A A264443 _Peter Bala_, Nov 13 2015