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A014739 Expansion of (1+x^2)/(1-2*x+x^3). +0
2
1, 2, 5, 9, 16, 27, 45, 74, 121, 197, 320, 519, 841, 1362, 2205, 3569, 5776, 9347, 15125, 24474, 39601, 64077, 103680, 167759, 271441, 439202, 710645, 1149849, 1860496, 3010347, 4870845, 7881194, 12752041, 20633237, 33385280, 54018519, 87403801 (list; graph; listen)
OFFSET

0,2

COMMENT

Number of wedged n-spheres in the homotopy type of the Boolean complex of the affine Coxeter group A~ _n. - Bridget Eileen Tenner (bridget(AT)math.depaul.edu), Jun 04 2008

REFERENCES

K. Ragnarsson and B. E. Tenner, Homotopy type of the Boolean complex of a Coxeter system

FORMULA

Partial sums of Lucas numbers A000032 less 1. G.f.: (1+x^2)/((1-x)(1-x-x^2)); a(n)=((3+sqrt(5))((1+sqrt(5))/2)^n+(3-sqrt(5))((1-sqrt(5))/2)^n)/2-2. - Paul Barry (pbarry(AT)wit.ie), Sep 03 2003

a(n)=A001610(n+1)-1 A014739(n). a(n)=F(n)+F(n+2)-2 {where F(n) is the n-th Fibonacci number} - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008

EXAMPLE

The Boolean complex of the affine Coxeter group \widetilde{A}_3 is homotopy equivalent to the wedge of 5 3-spheres.

MAPLE

with(combinat): seq(fibonacci(n)+fibonacci(n+2)-2, n=1..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008

MATHEMATICA

CoefficientList[ Series[(1 + x^2)/(1 - 2*x + x^3), {x, 0, 35}], x] (from Robert G. Wilson v Feb 25 2005)

CROSSREFS

Sequence in context: A007979 A097701 A056870 this_sequence A039946 A130752 A059529

Adjacent sequences: A014736 A014737 A014738 this_sequence A014740 A014741 A014742

KEYWORD

nonn

AUTHOR

njas

EXTENSIONS

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 25 2005

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


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