A036257 Number of inequivalent strings of 2n digits, when 2 strings are equivalent if turning 1 upside down gives the other.

1, 90, 9700, 992250, 99805000, 9995118750, 999877937500, 99996948281250, 9999923706250000, 999998092652343750, 99999952316289062500, 9999998807907128906250, 999999970197677734375000, 99999999254941940917968750, 9999999981373548510742187500

Offset

0,2

References

N. G. de Bruijn, Polya's theory of counting, in Beckenbach, ed., Applied Combinatorial Math., Wiley, 1964 (p. 182).

J.-P. Delahaye, 'Le miraculeux "lemme de Burnside"','La bande de chiffres' pp 146 in 'Pour la Science' (French edition of 'Scientific American') No.350 December 2006 Paris.

Links

Colin Barker, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (130,-3125,12500).

Formula

a(n) = 10^(2*n) - 5^(2*n)/2 + 5^n/2.

From Colin Barker, Jul 03 2017: (Start)

G.f.: (1 - 40*x + 1125*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)

Prog

(PARI) Vec((1 - 40*x + 1125*x^2) / ((1 - 5*x)*(1 - 25*x)*(1 - 100*x)) + O(x^30)) \\ Colin Barker, Jul 03 2017

Crossrefs

Cf. A036255, A036258.

Sequence in context: A166822 A166804 A116273 * A276352 A203779 A359842

Adjacent sequences: A036254 A036255 A036256 * A036258 A036259 A036260

Keyword

nonn,easy,base

Author

N. J. A. Sloane

Status

approved