A164498 Number of binary strings of length n with no substrings equal to 0010 0110 or 1100

13, 21, 33, 53, 84, 135, 217, 352, 570, 925, 1498, 2427, 3927, 6355, 10279, 16630, 26902, 43527, 70424, 113952, 184379, 298341, 482729, 781082, 1263815, 2044899, 3308703, 5353590, 8662271, 14015848, 22678105, 36693960, 59372075, 96066068

Offset

4,1

Links

R. H. Hardin, Table of n, a(n) for n = 4..500

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

Formula

G.f. -x^4*(13-5*x-9*x^2+13*x^3-6*x^4+4*x^5+8*x^6) / ( (x^2+x-1)*(x^5-x^4+x^3-x+1) ). - R. J. Mathar, Jan 19 2011

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1; 1, 0, -1, 2, -2, 0, 2]^(n-4)*[13; 21; 33; 53; 84; 135; 217])[1, 1] \\ Charles R Greathouse IV, Aug 05 2015

Crossrefs

Sequence in context: A164442 A164488 A164436 * A164485 A164447 A057200

Adjacent sequences: A164495 A164496 A164497 * A164499 A164500 A164501

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Status

approved