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A164481
Number of binary strings of length n with no substrings equal to 0001 0110 or 1101.
1
13, 21, 34, 53, 84, 131, 204, 318, 493, 766, 1188, 1842, 2857, 4428, 6865, 10641, 16493, 25565, 39623, 61414, 95187, 147531, 228662, 354404, 549295, 851357, 1319523, 2045140, 3169774, 4912854, 7614464, 11801703, 18291535, 28350160, 43940087
OFFSET
4,1
FORMULA
G.f.: -x^4*(-13+5*x+8*x^2+2*x^3-12*x^4+8*x^5) / ( (x-1)*(x^5-x^4+x^2+x-1) ). - R. J. Mathar, Jan 19 2011
a(n) = 2*a(n-1)-a(n-3)-a(n-4)+2*a(n-5)-a(n-6). - Wesley Ivan Hurt, Jan 16 2022
MATHEMATICA
LinearRecurrence[{2, 0, -1, -1, 2, -1}, {13, 21, 34, 53, 84, 131}, 50] (* Harvey P. Dale, Jul 03 2020 *)
CROSSREFS
Sequence in context: A164454 A164426 A164473 * A164433 A164479 A164497
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 14 2009
STATUS
approved