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A089645
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Given a stack of n coins, flip the top coin, then the stack of the top two coins, then the stack of the top three etc... starting again with the top coin after flipping all n coins. A flip of m coins reverses their order and inverts their state. This is the number of flips required to restore the stack to its original configuration.
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0
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2, 3, 9, 11, 24, 35, 28, 31, 80, 60, 121, 119, 116, 195, 75, 79, 204, 323, 228, 199, 146, 264, 529, 504, 200, 675, 540, 251, 840, 899, 186, 191, 1088, 748, 1225, 324, 740, 1140, 1521, 1079, 1680, 336, 1204, 484, 540, 460, 1692, 1151, 734, 2499
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Here "original configuration" seems to mean each coin in original orientation and either original or reverse order; for the original order and either original or reverse orientation n*A002326(n) flips required, while for both original order and original orientation n*A003558(n) required. - Henry Bottomley (se16(AT)btinternet.com), Jan 19 2007
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REFERENCES
| B. B. Newman, The Flippin' Coins Problem, Mathematics Magazine, Vol. 54 (1981), pp. 51-59.
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FORMULA
| For n>1, if A002326(n)=A003558(n) then a(n)=n*A002326(n), otherwise a(n)=n*A002326(n)-1. - Henry Bottomley (se16(AT)btinternet.com), Jan 19 2007
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EXAMPLE
| For 3 coins (starting with HHH) the flips move the stack through the sequence: HHH -1-> THH -2-> THH -3-> TTH -1-> HTH -2-> HTH -3-> THT -1-> HHT -2-> TTT -3-> HHH. (-n-> indicates n coins are flipped)
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CROSSREFS
| Cf. A056951.
Sequence in context: A049618 A057292 A098016 * A088086 A088084 A168080
Adjacent sequences: A089642 A089643 A089644 * A089646 A089647 A089648
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Richard Forster (gbrl01(AT)yahoo.co.uk), Jan 02 2004
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