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Search: id:A118646
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| A118646 |
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a(n) is the number of binary strings of length n such that there exists a subsequence of length 4 containing 3 or more ones. |
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+0
4
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| 0, 0, 1, 5, 13, 31, 71, 159, 346, 739, 1559, 3258, 6756, 13922, 28547, 58300, 118668, 240880, 487835, 986085, 1990025, 4010658, 8073786, 16237521, 32629241, 65522823, 131498801, 263774439, 528880599, 1060044148, 2124001923
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Or there are 3 ones in a row - this is relevant only for a(3).
Complementary to A118647, namely a(n) = 2^(n+3) - A118647(n).
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FORMULA
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a(n) = a(n-1) + a(n-2) + a(n-4) - a(n-6) + 13*2^(n-6)
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EXAMPLE
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a(4) is 5 because only the following binary strings of length 4 satisfy the conditions: 0111, 1011, 1101, 1011, 1111.
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CROSSREFS
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Sequence in context: A023261 A109419 A067333 this_sequence A097969 A082280 A007708
Adjacent sequences: A118643 A118644 A118645 this_sequence A118647 A118648 A118649
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KEYWORD
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nonn
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AUTHOR
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Tanya Khovanova (tanyakh(AT)yahoo.com), May 10 2006, Aug 17 2006
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