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A145112 Numbers of length n binary words with fewer than 4 0-digits between any pair of consecutive 1-digits. 3
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, 3226097530, 6218502938 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

T. Langley, J. Liese, J. Remmel, Generating Functions for Wilf Equivalence Under Generalized Factor Order, J. Int. Seq. 14 (2011) # 11.4.2

FORMULA

G.f.: (1-x+x^5)/(1-3*x+2*x^2+x^5-x^6).

EXAMPLE

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.

MAPLE

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..40);

MATHEMATICA

CoefficientList[Series[(1 - x + x^5) / (1 - 3 x + 2 x^2 + x^5 - x^6), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 06 2013 *)

CROSSREFS

4th column of A145111.

Cf. A242234.

Sequence in context: A051040 A006261 A290987 * A062259 A001949 A210031

Adjacent sequences:  A145109 A145110 A145111 * A145113 A145114 A145115

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Oct 02 2008

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)