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

0, 28, 112, 252, 448, 700, 1008, 1372, 1792, 2268, 2800, 3388, 4032, 4732, 5488, 6300, 7168, 8092, 9072, 10108, 11200, 12348, 13552, 14812, 16128, 17500, 18928, 20412, 21952, 23548, 25200, 26908, 28672, 30492, 32368, 34300, 36288, 38332

Offset: 0

Author

Roberto E. Martinez II, Oct 18 2001

Keywords

• nonn
• easy

Comments

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

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

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Similar sequences are listed in A244630.

Cf. A000217, A000290, A001105, A016742, A033428, A033581, A033582, A033583.

Cf. A144555, A135628.

Programs

Magma

[28*n^2: n in [0..40]]; // Vincenzo Librandi, Mar 30 2015

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

Mathematica

CoefficientList[Series[28 x (1 + x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 30 2015 *)

PARI

a(n)=28*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 56*n + a(n-1) - 28 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010

a(n) = 28*A000290(n) = 14*A001105(n) = 7*A016742(n) = 4*A033582(n) = 2*A144555(n). - Omar E. Pol, Jul 03 2014

From Vincenzo Librandi, Mar 30 2015: (Start)

G.f.: 28*x*(1+x)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

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

From Elmo R. Oliveira, Dec 01 2024: (Start)

E.g.f.: 28*x*(1 + x)*exp(x).

a(n) = n*A135628(n). (End)