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A052951 Expansion of (1+x-2x^2)/(1-2x)^2. 4
1, 5, 14, 36, 88, 208, 480, 1088, 2432, 5376, 11776, 25600, 55296, 118784, 253952, 540672, 1146880, 2424832, 5111808, 10747904, 22544384, 47185920, 98566144, 205520896, 427819008, 889192448, 1845493760, 3825205248, 7918845952 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals binomial transform of A042948 starting with "1": (1, 4, 5, 8, 9, 12, 13,...) = terms >0, == 0 or 1 mod 4. [From Gary W. Adamson, Feb 07 2009]

LINKS

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

O. Aichholzer, A. Asinowski, T. Miltzow, Disjoint compatibility graph of non-crossing matchings of points in convex position, arXiv preprint arXiv:1403.5546, 2014

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1021

Index entries for linear recurrences with constant coefficients, signature (4,-4).

FORMULA

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

Recurrence: {a(0)=1, 4*a(n)-4*a(n+1)+a(n+2)=0, a(1)=5, a(2)=14}

2^n*n+2^n+2^(n-1), n>0.

a(n) = A118413(n+1,n-1) for n>2. - Reinhard Zumkeller, Apr 27 2006

MAPLE

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

MATHEMATICA

CoefficientList[Series[-(-x+2*x^2-1)/(-1+2*x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 22 2012 *)

PROG

(MAGMA) I:=[1, 5, 14]; [n le 3 select I[n] else 4*Self(n-1)-4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 22 2012

CROSSREFS

Cf. A042948 [From Gary W. Adamson, Feb 07 2009]

Sequence in context: A193557 A187198 A097507 * A048745 A224716 A127980

Adjacent sequences:  A052948 A052949 A052950 * A052952 A052953 A052954

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified December 4 21:09 EST 2016. Contains 278755 sequences.