A164413 Number of binary strings of length n with no substrings equal to 0000, 0001 or 1001.

1, 2, 4, 8, 13, 22, 36, 58, 94, 152, 246, 398, 644, 1042, 1686, 2728, 4414, 7142, 11556, 18698, 30254, 48952, 79206, 128158, 207364, 335522, 542886, 878408, 1421294, 2299702, 3720996, 6020698, 9741694, 15762392, 25504086, 41266478, 66770564, 108037042

Offset

0,2

Comments

Essentially the same as A022112. - R. J. Mathar, Nov 30 2011

Links

David A. Corneth, Table of n, a(n) for n = 0..1999 (terms n = 4..500 from R. H. Hardin)

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

Formula

From Colin Barker, Oct 27 2017: (Start)

G.f.: -(x^2+1)*(x^2-x+1)*(x+1)^2/(x^2+x-1).

a(n) = 2*(((1 - sqrt(5))/2)^n + ((1 + sqrt(5))/2)^n) for n>4.

a(n) = a(n-1) + a(n-2) for n>6.

(End)

Prog

(PARI) Vec(-(x^2+1)*(x^2-x+1)*(x+1)^2/(x^2+x-1) + O(x^50)) \\ Colin Barker, Oct 27 2017
(PARI) first(n) = {my(start = [1, 2, 4, 8, 13, 22, 36]); if(n <= 7, return(vector(n+1, i, start[i]))); res = concat(start, vector(n-7)); for(i=8, n,
res[i] = res[i-1] + res[i-2]); res} \\ David A. Corneth, Oct 27 2017

Crossrefs

Sequence in context: A291553 A330153 A244985 * A164441 A338761 A023600

Adjacent sequences: A164410 A164411 A164412 * A164414 A164415 A164416

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Status

approved