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A064763 a(n) = 28*n^2. 3

%I

%S 0,28,112,252,448,700,1008,1372,1792,2268,2800,3388,4032,4732,5488,

%T 6300,7168,8092,9072,10108,11200,12348,13552,14812,16128,17500,18928,

%U 20412,21952,23548,25200,26908,28672,30492,32368,34300,36288,38332

%N a(n) = 28*n^2.

%C Number of edges in a complete 8-partite graph of order 8n, K_n,n,n,n,n,n,n,n.

%C 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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 56*n+a(n-1)-28 (with a(0)=0). - _Vincenzo Librandi_, Aug 07 2010

%F a(n) = 28*A000290(n) = 14*A001105(n) = 7*A016742(n) = 4*A033582(n) = 2*A144555(n). - _Omar E. Pol_, Jul 03 2014

%F G.f.: 28*x*(1+x)/(1-x)^3. - _Vincenzo Librandi_, Mar 30 2015

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Mar 30 2015

%F 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

%t CoefficientList[Series[28 x (1 + x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 30 2015 *)

%o (MAGMA) [28*n^2: n in [0..40]] /* or */ 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 (PARI) a(n)=28*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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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)