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A145114 Numbers of length n binary words with fewer than 6 0-digits between any pair of consecutive 1-digits. 2
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, 7001175484 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: (1-x+x^7)/(1-3*x+2*x^2+x^7-x^8).
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.
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);
MATHEMATICA
CoefficientList[Series[(1 - x + x^7) / (1 - 3 x + 2 x^2 + x^7 - x^8), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{3, -2, 0, 0, 0, 0, -1, 1}, {1, 2, 4, 8, 16, 32, 64, 128}, 40] (* Harvey P. Dale, Mar 13 2023 *)
CROSSREFS
6th column of A145111.
Sequence in context: A216264 A054045 A008860 * A172317 A234589 A079262
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Oct 02 2008
STATUS
approved

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Last modified June 17 03:50 EDT 2024. Contains 373432 sequences. (Running on oeis4.)