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A243815 Number of length n words on alphabet {0,1} such that the length of every maximal block of 0's (runs) is the same. 2
1, 2, 4, 8, 14, 24, 39, 62, 97, 151, 233, 360, 557, 864, 1344, 2099, 3290, 5176, 8169, 12931, 20524, 32654, 52060, 83149, 133012, 213069, 341718, 548614, 881572, 1417722, 2281517, 3673830, 5918958, 9540577, 15384490, 24817031, 40045768, 64637963, 104358789 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of terms of A164710 with exactly n+1 binary digits. - Robert Israel, Nov 09 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

0110 is a "good" word because the length of both its runs of 0's is 1.

Words of the form 11...1 are good words because the condition is vacuously satisfied.

a(5) = 24 because there are 32 length 5 binary words but we do not count: 00010, 00101, 00110, 01000, 01001, 01100, 10010, 10100.

MAPLE

a:= n-> 1 + add(add((d-> binomial(d+j, d))(n-(i*j-1))

          , j=1..iquo(n+1, i)), i=2..n+1):

seq(a(n), n=0..50);  # Alois P. Heinz, Jun 11 2014

MATHEMATICA

nn=30; Prepend[Map[Total, Transpose[Table[Drop[CoefficientList[Series[ (1+x^k)/(1-x-x^(k+1))-1/(1-x), {x, 0, nn}], x], 1], {k, 1, nn}]]], 0]+1

CROSSREFS

Cf. A164710.

Sequence in context: A281968 A091774 A280874 * A060046 A053801 A091778

Adjacent sequences:  A243812 A243813 A243814 * A243816 A243817 A243818

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jun 11 2014

STATUS

approved

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Last modified December 14 01:15 EST 2019. Contains 329977 sequences. (Running on oeis4.)