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A091573
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Poincaré series [or Poincare series] of the preprojective algebra of an extended Dynkin diagram of type E_6.
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7
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7, 12, 17, 24, 31, 36, 41, 48, 55, 60, 65, 72, 79, 84, 89, 96, 103, 108, 113, 120, 127, 132, 137, 144, 151, 156, 161, 168, 175, 180, 185, 192, 199, 204, 209, 216, 223, 228, 233, 240, 247, 252, 257, 264, 271, 276, 281, 288, 295, 300, 305, 312, 319, 324, 329
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listen;
history;
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internal format)
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OFFSET
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0,1
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REFERENCES
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I. Reiten, Dynkin diagrams and the representation theory of algebras, Notices of the AMS, Vol. 44, Number 5.
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LINKS
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FORMULA
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a(n) = 6*n+6 (n odd), 6*n+7 (n==0 (mod 4)), 6*n+5 (n==2 (mod 4)).
G.f.: (7-2*x+7*x^2) / ((1+x^2)*(1-x)^2).
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>3.
a(n) = (12+(-i)^n+i^n+12*n)/2 where i = sqrt(-1).
(End)
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MATHEMATICA
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CoefficientList[ Series[ (7 - 2x + 7x^2) / (1 - 2x + 2x^2 - 2x^3 + x^4), {x, 0, 49}], x] (* Jean-François Alcover, Dec 02 2011 *)
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PROG
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(PARI) a(n) = (12+(-I)^n+I^n+12*n)/2 \\ Colin Barker, Oct 18 2015
(PARI) Vec((7-2*x+7*x^2)/((1+x^2)*(1-x)^2) + O(x^100)) \\ Colin Barker, Oct 18 2015
(PARI) a(n) = if(n%2 == 1, 6*n+6, if(n%4 == 0, 6*n+7, 6*n+5));
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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