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A036257 Number of inequivalent strings of 2n digits, when 2 strings are equivalent if turning 1 upside down gives the other. 3
1, 90, 9700, 992250, 99805000, 9995118750, 999877937500, 99996948281250, 9999923706250000, 999998092652343750, 99999952316289062500, 9999998807907128906250, 999999970197677734375000, 99999999254941940917968750, 9999999981373548510742187500 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A166822 A166804 A116273 * A276352 A203779 A359842
KEYWORD
nonn,easy,base
AUTHOR
STATUS
approved

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Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)