A164418 Number of binary strings of length n with no substrings equal to 0000 0010 or 0101.

13, 22, 38, 66, 115, 200, 347, 601, 1042, 1808, 3137, 5442, 9440, 16375, 28405, 49274, 85476, 148275, 257211, 446181, 773986, 1342627, 2329044, 4040173, 7008453, 12157502, 21089513, 36583796, 63461595, 110086280, 190965717, 331266576

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 (1,0,1,1,1,1,1).

Formula

G.f.: -x^4*(13+9*x+16*x^2+15*x^3+14*x^4+12*x^5+8*x^6) / ( (x^2-x+1)*(x^5+2*x^4+2*x^3+x^2-1) ). - R. J. Mathar, Nov 30 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, 1, 1, 1, 1, 0, 1]^(n-4)*[13; 22; 38; 66; 115; 200; 347])[1, 1] \\ Charles R Greathouse IV, Jun 05 2026

Crossrefs

Sequence in context: A164421 A164493 A164445 * A301788 A164409 A301962

Adjacent sequences: A164415 A164416 A164417 * A164419 A164420 A164421

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Status

approved