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Search: id:A036258
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| A036258 |
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Number of inequivalent strings of n digits, when 2 strings are equivalent if turning 1 upside down gives the other. |
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+0
3
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| 1, 9, 90, 945, 9700, 98475, 992250, 9961125, 99805000, 999024375, 9995118750, 99975590625, 999877937500, 9999389671875, 99996948281250, 999984741328125, 9999923706250000, 99999618530859375, 999998092652343750, 9999990463259765625
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Nick Baxter, The Burnside di-lemma: combinatorics and puzzle symmetry, in Tribute to a Mathemagician, Peters, 2005, pp. 199-210.
De Bruijn, Polya's theory of counting, in Beckenbach, ed., Applied Combinatorial Math., Wiley, 1964 (p. 182).
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FORMULA
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a(n+1) = (1/10)*{10^n - 5^n + (4-(-1)^n)*5^[n/2]} (De Bruijn)
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MAPLE
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f:=n-> if n mod 2 = 0 then 10^n-(5^n-5^(n/2))/2 else 10^n-(5^n-3*5^((n-1)/2))/2; fi;
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CROSSREFS
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Cf. A036255, A036257.
Sequence in context: A052386 A057092 A052268 this_sequence A098399 A082367 A049389
Adjacent sequences: A036255 A036256 A036257 this_sequence A036259 A036260 A036261
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KEYWORD
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nonn,easy,base
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AUTHOR
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njas
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