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A219355 Size of the edge set of the Generalized Lucas Cube Q_n(111). 1
0, 1, 4, 9, 16, 40, 90, 189, 400, 828, 1690, 3421, 6864, 13676, 27090, 53385, 104736, 204680, 398610, 773889, 1498320, 2893632, 5575658, 10721381, 20577072, 39424100, 75412714, 144040437, 274743952, 523380516, 995841570, 1892692817, 3593501760, 6816026448, 12916524962, 24455934265, 46266661008, 87461480600, 165214492666 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

A. Ilic, S. Klavzar, Y. Rho, Generalized Lucas Cubes, Appl. An. Disc. Math. 6 (2012) 82-94. Proposition 11.

Index entries for linear recurrences with constant coefficients, signature (2,1,0,-3,-2,-1).

FORMULA

G.f.: x*(1+2*x-6*x^3+2*x^4+8*x^5+5*x^6+2*x^7)/(1-x-x^2-x^3)^2.  - Colin Barker, Nov 21 2012

MAPLE

VG := proc(n)

    option remember;

    if n <= 5 then

        op(n+1, [1, 2, 4, 7, 11, 21]) ;

    else

        procname(n-1)+procname(n-2)+procname(n-3) ;

    end if;

end proc:

EG := proc(n)

    option remember;

    if n <= 5 then

        op(n+1, [0, 1, 4, 9, 16, 40]) ;

    else

        procname(n-1)+procname(n-2)+procname(n-3)+VG(n-2)+2*VG(n-3) ;

    end if;

end proc:

seq(EG(n), n=0..60) ;

MATHEMATICA

CoefficientList[Series[x*(2*x^7+5*x^6+8*x^5+2*x^4-6*x^3+2*x+1)/(x^3+x^2+ x-1)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 23 2012 *)

PROG

(PARI) my(x='x+O('x^40)); concat([0], Vec(x*(1+2*x-6*x^3+2*x^4+8*x^5 +5*x^6+2*x^7)/(1-x-x^2-x^3)^2)) \\ G. C. Greubel, Apr 23 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( x*(1+2*x-6*x^3+2*x^4+8*x^5 +5*x^6+2*x^7)/(1-x-x^2-x^3)^2 )); // G. C. Greubel, Apr 23 2019

(Sage) (x*(1+2*x-6*x^3+2*x^4+8*x^5 +5*x^6+2*x^7)/(1-x-x^2-x^3)^2 ).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019

CROSSREFS

Cf. A001644 (vertex set).

Sequence in context: A250029 A111378 A106313 * A291216 A074101 A034377

Adjacent sequences:  A219352 A219353 A219354 * A219356 A219357 A219358

KEYWORD

easy,nonn

AUTHOR

R. J. Mathar, Nov 19 2012

STATUS

approved

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Last modified April 17 11:26 EDT 2021. Contains 343064 sequences. (Running on oeis4.)