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 A064762 #38 Nov 30 2024 13:01:04
%S A064762 0,21,84,189,336,525,756,1029,1344,1701,2100,2541,3024,3549,4116,4725,
%T A064762 5376,6069,6804,7581,8400,9261,10164,11109,12096,13125,14196,15309,
%U A064762 16464,17661,18900,20181,21504,22869,24276,25725,27216,28749
%N A064762 a(n) = 21*n^2.
%C A064762 Number of edges in a complete 7-partite graph of order 7n, K_n,n,n,n,n,n,n.
%H A064762 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A064762 a(n) = 42*n + a(n-1) - 21 for n > 0, a(0)=0. - _Vincenzo Librandi_, Aug 07 2010
%F A064762 a(n) = 21*A000290(n) = 7*A033428(n) = 3*A033582(n). - _Omar E. Pol_, Jul 03 2014
%F A064762 a(n) = t(7*n) - 7*t(n), where t(i) = i*(i+k)/2 for any k. Special case (k=1): a(n) = A000217(7*n) - 7*A000217(n). - _Bruno Berselli_, Aug 31 2017
%F A064762 From _Elmo R. Oliveira_, Nov 30 2024: (Start)
%F A064762 G.f.: 21*x*(1 + x)/(1-x)^3.
%F A064762 E.g.f.: 21*x*(1 + x)*exp(x).
%F A064762 a(n) = n*A008603(n) = A195049(2*n).
%F A064762 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A064762 21 Range[0, 50]^2 (* _Wesley Ivan Hurt_, Jul 04 2014 *)
%t A064762 LinearRecurrence[{3,-3,1},{0,21,84},40] (* _Harvey P. Dale_, Jul 29 2019 *)
%o A064762 (Magma) [21*n^2 : n in [0..50]]; // _Wesley Ivan Hurt_, Jul 04 2014
%o A064762 (PARI) a(n)=21*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A064762 Similar sequences are listed in A244630.
%Y A064762 Cf. A000217, A000290, A033428, A033581, A033582, A033583.
%Y A064762 Cf. A008603, A195049.
%K A064762 nonn,easy
%O A064762 0,2
%A A064762 _Roberto E. Martinez II_, Oct 18 2001