login
A373080
a(n) is the number of binary strings of length n not containing the substrings 0000, 0001, 0011, 0111, 1111.
2
1, 2, 4, 8, 11, 18, 28, 40, 64, 96, 144, 224, 336, 512, 784, 1184, 1808, 2752, 4176, 6368, 9680, 14720, 22416, 34080, 51856, 78912, 120016, 182624, 277840, 422656, 643088, 978336, 1488400, 2264512, 3445072, 5241312, 7974096, 12131456, 18456720, 28079648
OFFSET
0,2
FORMULA
a(n) = a(n-2) + 2*a(n-3) for n >= 7.
G.f.: -(x+1)^2*(x^2+1)^2/(2*x^3+x^2-1). - Alois P. Heinz, Jun 03 2024
MATHEMATICA
LinearRecurrence[{0, 1, 2}, {1, 2, 4, 8, 11, 18, 28}, 50] (* Paolo Xausa, Jun 24 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Miquel A. Fiol, Jun 03 2024
STATUS
approved