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A265050
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Poincaré series for hyperbolic reflection group with Coxeter diagram shown in Comments.
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1
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1, 4, 10, 21, 39, 68, 114, 186, 298, 472, 743, 1165, 1822, 2844, 4434, 6908, 10758, 16749, 26071, 40576, 63146, 98266, 152914, 237948, 370263, 576149, 896514, 1395012, 2170690, 3377668, 5255762, 8178133, 12725431, 19801164, 30811218, 47943194, 74601066, 116081520, 180626359, 281060077
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OFFSET
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0,2
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COMMENTS
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The Coxeter diagram is:
o---o
|...|
|...| 4
|...|
o---o
(4 nodes, square, one edge carries label 4)
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LINKS
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FORMULA
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G.f.: -b(2)*b(4)*(x^3+1)/t1 where b(k) = (1-x^k)/(1-x) and t1 = (x-1)*(x^6-x^5-x^4+x^3-x^2-x+1).
G.f.: (1+x)^3*(1-x+x^2)*(1+x^2) / ((1-x)*(1-x-x^2+x^3-x^4-x^5+x^6)). - Colin Barker, Jan 01 2016
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MATHEMATICA
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Join[{1}, LinearRecurrence[{2, 0, -2, 2, 0, -2, 1}, {4, 10, 21, 39, 68, 114, 186}, 40]] (* Jean-François Alcover, Jan 07 2019 *)
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PROG
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(PARI) Vec((1+x)^3*(1-x+x^2)*(1+x^2)/((1-x)*(1-x-x^2+x^3-x^4-x^5+x^6)) + O(x^50)) \\ Colin Barker, Jan 01 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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