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

Author

Clark Kimberling

Keywords

• nonn

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].

Examples

			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)
		

Formula

a(n) = Fibonacci(n+6) - 4*n - 8. - Ralf Stephan, Feb 15 2004