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 A118891 Number of binary sequences of length n with no subsequence 01110. 2
 1, 2, 4, 8, 16, 31, 60, 116, 223, 428, 820, 1569, 3002, 5744, 10992, 21039, 40273, 77095, 147588, 282538, 540881, 1035440, 1982194, 3794602, 7264164, 13906079, 26620957, 50961552, 97557726, 186758657, 357519595, 684414146, 1310201570 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is a_4(n) in the Doroslovacki reference. LINKS Table of n, a(n) for n=0..32. R. Doroslovacki, Binary sequences without 011...110 (k-1 1's) for fixed k, Mat. Vesnik 46 (1994), no. 3-4, 93-98. FORMULA Empirical g.f.: -(x^8+x^7-x^5+2*x^4-x+1) / (x^9-x^7-x^6+4*x^5-2*x^4-2*x^2+3*x-1). - Colin Barker, Aug 11 2013 PROG (PARI) { a4(n) = 1 + sum(i=1, n, sum(j=0, n-i, sum(k=0, (n-i-j)\2, sum(l=0, (n-i-j-2*k)\4, binomial(i-1, j)*binomial(i-1-j, k)*binomial(i-1-j-2*k, l)*binomial(n-i-j-2*k-3*l+1, l+1))))) } CROSSREFS Cf. A000045, A005251, A049864. Sequence in context: A189075 A345372 A189077 * A107066 A141019 A210003 Adjacent sequences: A118888 A118889 A118890 * A118892 A118893 A118894 KEYWORD nonn AUTHOR Max Alekseyev, Jun 26 2007 EXTENSIONS More terms from Max Alekseyev, Sep 25 2009 STATUS approved

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Last modified December 9 18:33 EST 2023. Contains 367693 sequences. (Running on oeis4.)