login
A164315
Number of binary strings of length n with no substrings equal to 000 or 011.
2
1, 2, 4, 6, 9, 13, 18, 25, 34, 46, 62, 83, 111, 148, 197, 262, 348, 462, 613, 813, 1078, 1429, 1894, 2510, 3326, 4407, 5839, 7736, 10249, 13578, 17988, 23830, 31569, 41821, 55402, 73393, 97226, 128798, 170622, 226027, 299423, 396652, 525453, 696078, 922108
OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5000 (first 500 terms from R. H. Hardin)
FORMULA
G.f.: (x^2+x+1)/((x-1)*(x^3+x^2-1)). - R. J. Mathar, Nov 28 2011
EXAMPLE
All solutions for N=6
001001 001010 010010 010100 010101 100100 100101 101001 101010 110010
110100 110101 111001 111010 111100 111101 111110 111111
MATHEMATICA
CoefficientList[Series[(x^2 + x + 1)/((x - 1) (x^3 + x^2 - 1)), {x, 0, 44}], x] (* Michael De Vlieger, Oct 11 2017 *)
CROSSREFS
Cf. A171861 (essentially the same sequence).
Sequence in context: A088575 A177189 A026906 * A171861 A376876 A039900
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Aug 12 2009
EXTENSIONS
Edited by Alois P. Heinz, Oct 11 2017
STATUS
approved