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A145114
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Numbers of length n binary words with fewer than 6 0-digits between any pair of consecutive 1-digits.
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1
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1, 2, 4, 8, 16, 32, 64, 128, 255, 507, 1007, 1999, 3967, 7871, 15615, 30976, 61446, 121886, 241774, 479582, 951294, 1886974, 3742973, 7424501, 14727117, 29212461, 57945341, 114939389, 227991805, 452240638, 897056776, 1779386436, 3529560412
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (1-x+x^7)/(1-3*x+2*x^2+x^7-x^8).
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EXAMPLE
| a(8) = 255 = 2^8-1, because 10000001 is the only binary word of length 8 with not less than 6 0-digits between any pair of consecutive 1-digits.
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MAPLE
| a:= n-> (Matrix([[2, 1$7]]). Matrix(8, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$4, -1, 1][i] else 0 fi)^n)[1, 2]: seq (a(n), n=0..35);
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CROSSREFS
| 6th column of A145111.
Sequence in context: A089889 A054045 A008860 * A172317 A079262 A194631
Adjacent sequences: A145111 A145112 A145113 * A145115 A145116 A145117
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 02 2008
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