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A164468
Number of binary strings of length n with no substrings equal to 0001, 0100, or 1110.
1
13, 20, 30, 45, 67, 99, 146, 215, 316, 464, 681, 999, 1465, 2148, 3149, 4616, 6766, 9917, 14535, 21303, 31222, 45759, 67064, 98288, 144049, 211115, 309405, 453456, 664573, 973980, 1427438, 2092013, 3065995, 4493435, 6585450, 9651447, 14144884
OFFSET
4,1
FORMULA
G.f.: -x^4*(-13+6*x-3*x^2+8*x^3) / ( (x-1)*(x^3+x-1) ). - R. J. Mathar, Jan 19 2011
a(n) = a(n-1) + a(n-3) + 2 for n>6. - Greg Dresden, Feb 09 2020
MATHEMATICA
LinearRecurrence[{2, -1, 1, -1}, {13, 20, 30, 45}, 40] (* Harvey P. Dale, Aug 12 2023 *)
CROSSREFS
Sequence in context: A096277 A164475 A164483 * A164489 A164464 A164467
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 14 2009
STATUS
approved