A062258 -id:A062258 - cp's OEIS frontend

A062257 Number of (0,1)-strings of length n with no occurrences of the substrings 10101101 and 1110101.

1, 2, 4, 8, 16, 32, 64, 127, 251, 496, 981, 1940, 3837, 7590, 15015, 29704, 58763, 116249, 229971, 454942, 899991, 1780410, 3522102, 6967611, 13783703, 27267665, 53942368, 106711708, 211102869, 417615105, 826148769, 1634332138

Offset: 0

Vladeta Jovovic, Jun 14 2001

nonn

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (Example 2.8.11).

Cf. A062258, A062259.

G.f.: (1+x^5+x^6+x^7-x^9)/(1+x^5-x^6-x^9-2*x-x^8+x^10). a(n) = 2*a(n-1)-a(n-5)+a(n-6)+a(n-8)+a(n-9)-a(n-10).

A062259 Number of (0,1)-strings of length n that avoid the substrings of substrings 11101011 and 101111.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 63, 124, 243, 476, 933, 1830, 3590, 7043, 13818, 27110, 53186, 104342, 204701, 401588, 787846, 1545619, 3032243, 5948749, 11670441, 22895434, 44916973, 88119508, 172875575, 339152648, 665360153, 1305324126, 2560825244

Offset: 0

Vladeta Jovovic, Jun 14 2001

nonn

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(Problem 2.8.4).

Cf. A062257, A062258.

G.f.: (1+x+x^2+x^3+x^4+2*x^5+3*x^6+3*x^7+2*x^8+x^9)/(1-x-x^2-x^3-x^4-2*x^7-2*x^8-x^9-x^10). a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)+2*a(n-7)+2*a(n-8)+a(n-9)+a(n-10).

Goulden and Jackson give the g.f. in the equivalent form (1+x^5+x^6-x^8-x^9-x^10)/(1-2*x+x^5-2*x^7+x^9+x^11). - N. J. A. Sloane, Apr 09 2011

cp's OEIS Frontend

A062257 Number of (0,1)-strings of length n with no occurrences of the substrings 10101101 and 1110101.

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