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Search: id:A008346
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| A008346 |
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Fibonacci(n) + (-1)^n. |
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+0
13
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| 1, 0, 2, 1, 4, 4, 9, 12, 22, 33, 56, 88, 145, 232, 378, 609, 988, 1596, 2585, 4180, 6766, 10945, 17712, 28656, 46369, 75024, 121394, 196417, 317812, 514228, 832041, 1346268, 2178310, 3524577
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Diagonal sums of A059260. - Paul Barry (pbarry(AT)wit.ie), Oct 25 2004
The absolute value of the Euler characteristic of the Boolean complex of the Coxeter group A_n. - Bridget Eileen Tenner (bridget(AT)math.depaul.edu), Jun 04 2008
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REFERENCES
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K. Ragnarsson and B. E. Tenner, Homotopy type of the Boolean complex of a Coxeter system
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 445
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FORMULA
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G.f.: 1/(1-2*x^2-x^3). a(n) = 2a(n-2) + a(n-3).
a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, (-1)^(n-k-j)binomial(j, k)}}. Diagonal sums of A059260. - Paul Barry (pbarry(AT)wit.ie), Sep 23 2004
a(n)=sum{k=0..floor(n/2), binomial(k, n-2k)2^(3k-n)}; a(n)=sum{k=0..floor(n/2), binomial(k, n-2k)2^k(1/2)^(n-2k)}. - Paul Barry (pbarry(AT)wit.ie), Oct 04 2004
G.f. : 1/((1+x)(1-x-x^2); a(n)=sum{k=0..n, binomial(n-k-1, k)}. - Paul Barry (pbarry(AT)wit.ie), Oct 25 2004
a(n) = |1 + (-1)^{n-1}f(n-1)| - Bridget Eileen Tenner (bridget(AT)math.depaul.edu), Jun 04 2008
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EXAMPLE
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The Boolean complex of Coxeter group A_4 is homotopy equivalent to the wedge of 2 spheres S^3, which has Euler characteristic 1 - 2 = -1.
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MAPLE
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with(combinat): f := n->fibonacci(n)+(-1)^n;
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MATHEMATICA
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Table[Fibonacci[n]+(-1)^n, {n, 0, 22}] (Vladimir Orlovsky, Jul 22 2008)
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CROSSREFS
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Cf. A007492, A066983, A078024.
Cf. A119282.
Sequence in context: A060723 A074763 A099932 this_sequence A119282 A095293 A034409
Adjacent sequences: A008343 A008344 A008345 this_sequence A008347 A008348 A008349
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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