%I #17 Nov 09 2015 18:50:42
%S 1,2,4,8,14,24,39,62,97,151,233,360,557,864,1344,2099,3290,5176,8169,
%T 12931,20524,32654,52060,83149,133012,213069,341718,548614,881572,
%U 1417722,2281517,3673830,5918958,9540577,15384490,24817031,40045768,64637963,104358789
%N Number of length n words on alphabet {0,1} such that the length of every maximal block of 0's (runs) is the same.
%C Number of terms of A164710 with exactly n+1 binary digits. - _Robert Israel_, Nov 09 2015
%H Alois P. Heinz, <a href="/A243815/b243815.txt">Table of n, a(n) for n = 0..1000</a>
%e 0110 is a "good" word because the length of both its runs of 0's is 1.
%e Words of the form 11...1 are good words because the condition is vacuously satisfied.
%e a(5) = 24 because there are 32 length 5 binary words but we do not count: 00010, 00101, 00110, 01000, 01001, 01100, 10010, 10100.
%p a:= n-> 1 + add(add((d-> binomial(d+j, d))(n-(i*j-1))
%p , j=1..iquo(n+1, i)), i=2..n+1):
%p seq(a(n), n=0..50); # _Alois P. Heinz_, Jun 11 2014
%t 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
%Y Cf. A164710.
%K nonn
%O 0,2
%A _Geoffrey Critzer_, Jun 11 2014
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