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A145112
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Numbers of length n binary words with fewer than 4 0-digits between any pair of consecutive 1-digits.
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1
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1, 2, 4, 8, 16, 32, 63, 123, 239, 463, 895, 1728, 3334, 6430, 12398, 23902, 46077, 88821, 171213, 330029, 636157, 1226238, 2363656, 4556100, 8782172, 16928188, 32630139, 62896623, 121237147, 233692123, 450456059, 868281980, 1673667338
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..32.
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FORMULA
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G.f.: (1-x+x^5)/(1-3*x+2*x^2+x^5-x^6).
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EXAMPLE
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a(6) = 63 = 2^6-1, because 100001 is the only binary word of length 6 with not less than 4 0-digits between any pair of consecutive 1-digits.
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MAPLE
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a:= n-> (Matrix([[2, 1$5]]). Matrix(6, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$2, -1, 1][i] else 0 fi)^n)[1, 2]: seq (a(n), n=0..35);
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CROSSREFS
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4th column of A145111.
Sequence in context: A052396 A051040 A006261 * A062259 A001949 A210031
Adjacent sequences: A145109 A145110 A145111 * A145113 A145114 A145115
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Oct 02 2008
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STATUS
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approved
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