login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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]

REFERENCES

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

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1021

Index to sequences with 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

EXTENSIONS

More terms from James A. Sellers, Jun 08 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 25 23:44 EST 2014. Contains 250017 sequences.