A206278 Total number of triangles in Cayley graph Cay(Z_{2^n}, QR*(2^n)).

0, 0, 128, 1024, 6656, 53248, 387072, 3096576, 24092672, 192741376, 1530822656, 12246581248, 97793998848, 782351990784, 6255953838080, 50047630704640, 400335237545984, 3202681900367872, 25620722214764544, 204965777718116352, 1639714493699194880, 13117715949593559040, 104941539947077173248, 839532319576617385984

Offset

3,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

Reinaldo E. Giudici and Aurora A. Olivieri, Quadratic modulo 2n Cayley graphs, Discrete Math. 215 (2000), no. 1-3, 73-79. See T(n) in Theorem 3.1.

Index entries for linear recurrences with constant coefficients, signature (8,20,-160,-64,512).

Formula

G.f.: 128*x^5*(32*x^2-1) / ((2*x-1)*(2*x+1)*(4*x-1)*(4*x+1)*(8*x-1)). - Colin Barker, Jul 23 2013

Maple

f:=n-> if n mod 2 = 1 then
(1/45)*(2^(3*(n-1))+5*2^(2*n-1)-7*2^(n+2));
else
(1/45)*(2^(3*(n-1))+5*2^(2*n)-7*2^(n+4));
fi;
[seq(f(n), n=3..40)];

Mathematica

CoefficientList[Series[128 x^2 (32 x^2 - 1) / ((2 x - 1) (2 x + 1) (4 x - 1) (4 x + 1) (8 x - 1)), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 21 2016 *)
LinearRecurrence[{8, 20, -160, -64, 512}, {0, 0, 128, 1024, 6656}, 30] (* Harvey P. Dale, May 31 2019 *)

Crossrefs

Sequence in context: A183972 A143708 A130813 * A100628 A344303 A221599

Adjacent sequences: A206275 A206276 A206277 * A206279 A206280 A206281

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 05 2012

Status

approved