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 A064763 #45 Dec 02 2024 06:43:32
%S A064763 0,28,112,252,448,700,1008,1372,1792,2268,2800,3388,4032,4732,5488,
%T A064763 6300,7168,8092,9072,10108,11200,12348,13552,14812,16128,17500,18928,
%U A064763 20412,21952,23548,25200,26908,28672,30492,32368,34300,36288,38332
%N A064763 a(n) = 28*n^2.
%C A064763 Number of edges in a complete 8-partite graph of order 8n, K_n,n,n,n,n,n,n,n.
%C A064763 Sequence found by reading the line from 0, in the direction 0, 28, ..., in the square spiral whose vertices are the generalized 16-gonal numbers. - _Omar E. Pol_, Jul 03 2014
%H A064763 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A064763 a(n) = 56*n + a(n-1) - 28 (with a(0)=0). - _Vincenzo Librandi_, Aug 07 2010
%F A064763 a(n) = 28*A000290(n) = 14*A001105(n) = 7*A016742(n) = 4*A033582(n) = 2*A144555(n). - _Omar E. Pol_, Jul 03 2014
%F A064763 From _Vincenzo Librandi_, Mar 30 2015: (Start)
%F A064763 G.f.: 28*x*(1+x)/(1-x)^3.
%F A064763 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A064763 a(n) = t(8*n) - 8*t(n), where t(i) = i*(i+k)/2 for any k. Special case (k=1): a(n) = A000217(8*n) - 8*A000217(n). - _Bruno Berselli_, Aug 31 2017
%F A064763 From _Elmo R. Oliveira_, Dec 01 2024: (Start)
%F A064763 E.g.f.: 28*x*(1 + x)*exp(x).
%F A064763 a(n) = n*A135628(n). (End)
%t A064763 CoefficientList[Series[28 x (1 + x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 30 2015 *)
%o A064763 (Magma) [28*n^2: n in [0..40]]; // _Vincenzo Librandi_, Mar 30 2015
%o A064763 (Magma) I:=[0,28,112]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Mar 30 2015
%o A064763 (PARI) a(n)=28*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A064763 Similar sequences are listed in A244630.
%Y A064763 Cf. A000217, A000290, A001105, A016742, A033428, A033581, A033582, A033583.
%Y A064763 Cf. A144555, A135628.
%K A064763 nonn,easy
%O A064763 0,2
%A A064763 _Roberto E. Martinez II_, Oct 18 2001