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%I #8 Jul 03 2017 07:41:28
%S 9,945,98475,9961125,999024375,99975590625,9999389671875,
%T 999984741328125,99999618530859375,9999990463259765625,
%U 999999761581435546875,99999994039535595703125,9999999850988388427734375,999999996274709703369140625,99999999906867742547607421875
%N Number of inequivalent strings of 2n+1 digits, when 2 strings are equivalent if turning 1 upside down gives the other.
%D De Bruijn, Polya's theory of counting, in Beckenbach, ed., Applied Combinatorial Math., Wiley, 1964 (p. 182).
%H Colin Barker, <a href="/A036255/b036255.txt">Table of n, a(n) for n = 0..450</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (130,-3125,12500).
%F a(n) = 10^(2*n+1) - 5^(2*n+1)/2 + 3*5^n/2.
%F From _Colin Barker_, Jul 03 2017: (Start)
%F G.f.: 3*(3 - 75*x + 1250*x^2) / ((1 - 5*x)*(1 - 25*x)*(1 - 100*x)).
%F a(n) = 130*a(n-1) - 3125*a(n-2) + 12500*a(n-3) for n>2.
%F (End)
%o (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
%Y Cf. A036257, A036258.
%K nonn,easy,base
%O 0,1
%A _N. J. A. Sloane_
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