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A023652
Convolution of (F(2), F(3), F(4), ...) and odd numbers.
2
1, 5, 14, 31, 61, 112, 197, 337, 566, 939, 1545, 2528, 4121, 6701, 10878, 17639, 28581, 46288, 74941, 121305, 196326, 317715, 514129, 831936, 1346161, 2178197, 3524462, 5702767, 9227341, 14930224, 24157685, 39088033, 63245846, 102334011, 165579993, 267914144, 433494281, 701408573
OFFSET
1,2
COMMENTS
a(n) is the number of bit strings of length n+3 with the pattern 01 at least twice, and without the pattern 110, see example. [John M. Campbell, Jan 25 2013].
FORMULA
a(n) = Fibonacci(n+6) - 4*n - 8. - Ralf Stephan, Feb 15 2004
EXAMPLE
From John M. Campbell_, Jan 25 2013: (Start)
There are a(3) = 14 bit strings of length 3+3 with the pattern 01 at least twice, and without the pattern 110:
000101, 001001, 001010, 001011, 010001, 010010, 010011,
010100, 010101, 010111, 100101, 101001, 101010, 101011
(End)
CROSSREFS
Sequence in context: A299276 A267167 A360487 * A283523 A101648 A265100
KEYWORD
nonn
STATUS
approved