A164414 Number of binary strings of length n with no substrings equal to 0000, 0001, or 1010.

1, 2, 4, 8, 13, 22, 37, 63, 107, 181, 307, 521, 883, 1497, 2539, 4305, 7299, 12377, 20987, 35585, 60339, 102313, 173483, 294161, 498787, 845753, 1434075, 2431649, 4123155, 6991305, 11854603, 20100913, 34083523, 57792729, 97994555, 166161601, 281747059

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000 (terms n=4..500 from R. H. Hardin)

Index entries for linear recurrences with constant coefficients, signature (1,0,2).

Formula

From R. J. Mathar, Nov 30 2011: (Start)

a(n) = 13*A077949(n-4) + 9*A077949(n-5) + 15*A077949(n-6).

G.f.: (x^6-x^5-x^4-2*x^3-2*x^2-x-1)/(2*x^3+x-1).

(End)

Crossrefs

Cf. A077949.

Sequence in context: A164437 A164428 A164507 * A164411 A164443 A074467

Adjacent sequences: A164411 A164412 A164413 * A164415 A164416 A164417

Keyword

easy,nonn

Author

R. H. Hardin, Aug 14 2009

Extensions

a(0)-a(3) from Alois P. Heinz, Jun 10 2021

Status

approved