A023652 - OEIS

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

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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

Paolo Xausa, Table of n, a(n) for n = 1..1000

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)

MATHEMATICA

A023652[n_] := Fibonacci[n + 6] - 4*n - 8;