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%I #34 Sep 08 2022 08:45:04
%S 0,21,84,189,336,525,756,1029,1344,1701,2100,2541,3024,3549,4116,4725,
%T 5376,6069,6804,7581,8400,9261,10164,11109,12096,13125,14196,15309,
%U 16464,17661,18900,20181,21504,22869,24276,25725,27216,28749
%N a(n) = 21*n^2.
%C Number of edges in a complete 7-partite graph of order 7n, K_n,n,n,n,n,n,n.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 42*n+a(n-1)-21 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 07 2010
%F a(n) = 21*A000290(n) = 7*A033428(n) = 3*A033582(n). - _Omar E. Pol_, Jul 03 2014
%F 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
%t 21 Range[0, 50]^2 (* _Wesley Ivan Hurt_, Jul 04 2014 *)
%t LinearRecurrence[{3,-3,1},{0,21,84},40] (* _Harvey P. Dale_, Jul 29 2019 *)
%o (Magma) [21*n^2 : n in [0..50]]; // _Wesley Ivan Hurt_, Jul 04 2014
%o (PARI) a(n)=21*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000217, A000290, A033428, A033581, A033583.
%Y Similar sequences are listed in A244630.
%K nonn,easy
%O 0,2
%A _Roberto E. Martinez II_, Oct 18 2001
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