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Search: id:A080254
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| A080254 |
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For n>3, a(n) is the number of elements in the Coxeter complex of type D_n (although the sequence starts at n=0. See comments below for precise explanation). |
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+0
4
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| 1, 1, 9, 75, 865, 12483, 216113, 4364979, 100757313, 2616517443, 75496735057, 2396212835283, 82968104980961, 3112139513814243, 125716310807844081, 5441108944839913587, 251195548533025953409, 12321551453507301079683
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The sequence makes most sense when n>3. The values for a(2) and a(3) make sense if we regard D_2=A_1 x A_1 and D_3=A_3. The values for a(0) and a(1) have to be regarded as conventions, and were included to give a nice recursive description. The corresponding sequence for type B is A080253. There one can find a worked example as well as a geometric interpretation.
Also, Eulerian D-polynomials (A066094) evaluated at 2. - Ralf Stephan, Apr 23 2004
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REFERENCES
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Kenneth S. Brown, Buildings, Springer-Verlag, 1988
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FORMULA
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a(0)=a(1)=1. For n>1, a(n)=1 + sum('2^r*binomial(n, r)*a(n-r)', 'r'=1..n)
E.g.f: (2*x-exp(x))/(exp(2*x)-2) - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 14 2003
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CROSSREFS
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Cf. A000670, A080253.
Sequence in context: A136659 A126965 A066222 this_sequence A056339 A056329 A082677
Adjacent sequences: A080251 A080252 A080253 this_sequence A080255 A080256 A080257
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Boddington & Tim Honeywill (psb(AT)maths.warwick.ac.uk), Feb 10 2003
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 14 2003
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