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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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3
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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; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| 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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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-1,-2,1,-2,-1,2).
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FORMULA
| a(n) = a(n-1) + a(n-2) + a(n-4) - a(n-6) + 13*2^(n-6).
a(n)= +3*a(n-1) -a(n-2) -2*a(n-3) +a(n-4) -2*a(n-5) -a(n-6) +2*a(n-7).
G.f. x^3*(-1-2*x+x^2+x^3) / ( (2*x-1)*(x^6-x^4-x^2-x+1) ). - R. J. Mathar, Nov 28 2011
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EXAMPLE
| 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
| Sequence in context: A165888 A109419 A067333 * A097969 A082280 A007708
Adjacent sequences: A118643 A118644 A118645 * A118647 A118648 A118649
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KEYWORD
| nonn
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AUTHOR
| Tanya Khovanova (tanyakh(AT)yahoo.com), May 10 2006, Aug 17 2006
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