login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)