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A052953 Expansion of 2*(1-x-x^2)/((x-1)(2x-1)(1+x)). 6
2, 2, 4, 6, 12, 22, 44, 86, 172, 342, 684, 1366, 2732, 5462, 10924, 21846, 43692, 87382, 174764, 349526, 699052, 1398102, 2796204, 5592406, 11184812, 22369622, 44739244, 89478486, 178956972, 357913942, 715827884, 1431655766, 2863311532 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) = sum of absolute values of terms in the (n+1)-th row of the triangle in A108561; - Reinhard Zumkeller, Jun 10 2005

a(n) = A078008(n+1) + 2*(1 + n mod 2). - Reinhard Zumkeller, Jun 10 2005

Essentially the same as A128209. - R. J. Mathar, Jun 14 2008

LINKS

Table of n, a(n) for n=0..32.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1024

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

FORMULA

G.f.: -2*(-1+x+x^2)/(-1+x+2*x^2)/(-1+x).

Recurrence: {a(2)=4, a(1)=2, a(0)=2, -2*a(n)-a(n+1)+a(n+2)+2=0}.

1+Sum(1/9*(1+4*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+2*_Z^2)).

a(2n) = 2*a(n-1)-2, a(2n+1) = 2*a(2n). - Lee Hae-hwang, Oct 11 2002

a(n) = A001045(n+1)+1; a(n) = (2^(n+1)-(-1)^(n+1))/3+1. - Paul Barry, May 24 2004

MAPLE

spec := [S, {S=Union(Sequence(Union(Prod(Union(Z, Z), Z), Z)), Sequence(Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);

PROG

(Sage) from sage.combinat.sloane_functions import recur_gen2; it = recur_gen2(1, 1, 1, 2); [it.next()+1 for i in xrange(0, 34)] # Zerinvary Lajos, Jul 06 2008

CROSSREFS

Apart from initial term, equals A026644(n+1) + 2.

Cf. A001045.

Sequence in context: A216957 A122536 A238014 * A128209 A274935 A188538

Adjacent sequences:  A052950 A052951 A052952 * A052954 A052955 A052956

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

More terms from James A. Sellers, Jun 05 2000

STATUS

approved

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Last modified June 24 21:16 EDT 2019. Contains 324337 sequences. (Running on oeis4.)