A023652 - OEIS

A023652

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

%I #10 Jan 25 2013 03:24:40

%S 1,5,14,31,61,112,197,337,566,939,1545,2528,4121,6701,10878,17639,

%T 28581,46288,74941,121305,196326,317715,514129,831936,1346161,2178197,

%U 3524462,5702767,9227341,14930224,24157685,39088033,63245846,102334011,165579993,267914144,433494281,701408573

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

%C 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].

%F a(n) = Fibonacci(n+6) - 4*n - 8. - _Ralf Stephan_, Feb 15 2004

%e From John M. Campbell_, Jan 25 2013: (Start)

%e There are a(3) = 14 bit strings of length 3+3 with the pattern 01 at least twice, and without the pattern 110:

%e 000101, 001001, 001010, 001011, 010001, 010010, 010011,

%e 010100, 010101, 010111, 100101, 101001, 101010, 101011

%e (End)

%K nonn

%O 1,2

%A _Clark Kimberling_