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A265051
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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, 22, 44, 84, 156, 284, 512, 918, 1642, 2932, 5230, 9324, 16618, 29614, 52768, 94020, 167516, 298460, 531756, 947406, 1687946, 3007324, 5357986, 9546028, 17007626, 30301534, 53986540, 96184780, 171367004, 305314932, 543962400, 969147134, 1726674794, 3076319100, 5480904238
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OFFSET
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0,2
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COMMENTS
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The Coxeter diagram is:
..4
o---o
|...|
|...|
|...|
o---o
..4
(4 nodes, square, two opposite edges carry 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^2-x+1).
G.f.: (1+x)^3*(1-x+x^2)*(1+x^2) / ((1-x)*(1-x-x^2-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, -1, 1, 0, -2, 1}, {4, 10, 22, 44, 84, 156, 284}, 60]] (* Vincenzo Librandi, Jan 01 2016 *)
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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^4-x^5+x^6)) + O(x^50)) \\ Colin Barker, Jan 01 2016
(Magma) I:=[1, 4, 10, 22, 44, 84, 156, 284]; [n le 8 select I[n] else 2*Self(n-1)-Self(n-3)+Self(n-4)-2*Self(n-6)+Self(n-7): n in [1..50]]; // Vincenzo Librandi, 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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