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 A264444 #12 Sep 08 2022 08:46:14
%S A264444 0,20,48,85,132,190,260,343,440,552,680,825,988,1170,1372,1595,1840,
%T A264444 2108,2400,2717,3060,3430,3828,4255,4712,5200,5720,6273,6860,7482,
%U A264444 8140,8835,9568,10340,11152,12005,12900,13838,14820,15847,16920
%N A264444 a(n) = n*(n + 7)*(n + 14)/6.
%C A264444 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 = 7.
%H A264444 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A264444 O.g.f.: x*(13*x^2 - 32*x + 20)/(1 - x)^4.
%F A264444 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 A264444 seq( n*(n + 7)*(n + 14)/6, n = 0..40 );
%t A264444 Table[n (n + 7) (n + 14)/6, {n, 0, 40}] (* _Vincenzo Librandi_, Nov 16 2015 *)
%o A264444 (PARI) vector(100, n, n--; n*(n+7)*(n+14)/6) \\ _Altug Alkan_, Nov 15 2015
%o A264444 (Magma) [n*(n+7)*(n+14)/6: n in [0..40]]; // _Vincenzo Librandi_, Nov 16 2015
%Y A264444 Cf. A007310, A264443, A264445, A264446, A264447, A264448, A264449, A264450.
%K A264444 nonn,easy
%O A264444 0,2
%A A264444 _Peter Bala_, Nov 13 2015