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Search: id:A066345
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| A066345 |
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Winning binary "same game" templates of length n as defined below. |
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+0
4
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| 1, 1, 4, 7, 20, 39, 96, 191, 432, 863, 1856, 3711, 7744, 15487, 31744, 63487, 128768, 257535, 519168, 1038335, 2085888, 4171775, 8364032, 16728063, 33501184, 67002367, 134103040, 268206079, 536625152, 1073250303, 2146959360
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A "same game template" is a ternary number without digit 0 (A007931), where 2 represents any removable maximal run of identical bits, and ternary 1 represents remaining single bits, e.g. 211 for 0010, 1101, 00010, etc. A winning ternary template represents an infinite subset of winning binary "same games", e.g. 121 for 0110, 1001, 01110, etc.
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FORMULA
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a(2*n-1)= 2^(2*n-1) -n * 2^(n-1), a(2*n)= 2*a(2*n-1) -1.
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EXAMPLE
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There are a(3)= 4 winning templates 121, 122, 221, 222 with 3 ternary digits, and a(4)= 7 winning templates 1212, 2121, 1222, 2221, 2122, 2212, 2222.
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CROSSREFS
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a(2*n-1)= A008353(n-1), cf. A035615, A007931, A066067.
Sequence in context: A090879 A084404 A049947 this_sequence A026570 A111955 A039959
Adjacent sequences: A066342 A066343 A066344 this_sequence A066346 A066347 A066348
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KEYWORD
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nonn,easy
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AUTHOR
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Frank.Ellermann(AT)t-online.de, Dec 23 2001
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