A023652 Convolution of (F(2), F(3), F(4), ...) and odd numbers.

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].

Links

Table of n, a(n) for n=1..38.

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

Adjacent sequences: A023649 A023650 A023651 * A023653 A023654 A023655

Keyword

nonn

Author

Clark Kimberling

Status

approved