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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
OFFSET
0,2
COMMENTS
This is a_4(n) in the Doroslovacki reference.
LINKS
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
KEYWORD
nonn
AUTHOR
Max Alekseyev, Jun 26 2007
EXTENSIONS
More terms from Max Alekseyev, Sep 25 2009
STATUS
approved