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A036255
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Number of inequivalent strings of 2n+1 digits, when 2 strings are equivalent if turning 1 upside down gives the other.
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3
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9, 945, 98475, 9961125, 999024375, 99975590625, 9999389671875, 999984741328125, 99999618530859375, 9999990463259765625, 999999761581435546875, 99999994039535595703125, 9999999850988388427734375, 999999996274709703369140625, 99999999906867742547607421875
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OFFSET
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0,1
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REFERENCES
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De Bruijn, Polya's theory of counting, in Beckenbach, ed., Applied Combinatorial Math., Wiley, 1964 (p. 182).
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LINKS
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FORMULA
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a(n) = 10^(2*n+1) - 5^(2*n+1)/2 + 3*5^n/2.
G.f.: 3*(3 - 75*x + 1250*x^2) / ((1 - 5*x)*(1 - 25*x)*(1 - 100*x)).
a(n) = 130*a(n-1) - 3125*a(n-2) + 12500*a(n-3) for n>2.
(End)
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PROG
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(PARI) Vec(3*(3 - 75*x + 1250*x^2) / ((1 - 5*x)*(1 - 25*x)*(1 - 100*x)) + O(x^20)) \\ Colin Barker, Jul 03 2017
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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