cp's OEIS Frontend

A212234 Number of 0..2 arrays of length 1+2*n with sum no more than 2*n in any length 2n subsequence (=50% duty cycle).

%I A212234 #9 Jun 02 2025 07:56:04
%S A212234 14,124,1113,10002,89911,808403,7269626,65380788,588072207,5289869433,
%T A212234 47586806448,428105244789,3851528519268,34652238703192,
%U A212234 311776035394625,2805210936456962,25240510718260791,227111596463339585
%N A212234 Number of 0..2 arrays of length 1+2*n with sum no more than 2*n in any length 2n subsequence (=50% duty cycle).
%C A212234 Row 2 of A212232
%H A212234 R. H. Hardin, <a href="/A212234/b212234.txt">Table of n, a(n) for n = 1..210</a>
%F A212234 a(n) = [x^(2*n)] (1+z+z^2)^(2*n-1)*(1+3*z+5*z^2)/(1-z). - _Robert Israel_, Mar 06 2018
%e A212234 Some solutions for n=3
%e A212234 ..0....0....0....1....1....0....1....0....1....0....1....1....0....0....2....1
%e A212234 ..0....0....0....1....0....2....1....2....0....2....1....0....0....1....1....1
%e A212234 ..1....0....2....0....1....0....0....2....0....1....1....1....0....0....0....2
%e A212234 ..2....1....1....2....1....0....2....0....0....0....2....2....2....0....1....0
%e A212234 ..0....1....0....1....2....1....0....0....1....2....1....0....1....1....2....1
%e A212234 ..2....1....1....0....1....1....1....0....2....0....0....0....0....1....0....0
%e A212234 ..0....0....0....2....0....2....1....2....1....1....0....1....0....1....0....2
%p A212234 f:= proc(n) local S;
%p A212234    S:= series((1+z+z^2)^(2*n-1)*(1+3*z+5*z^2)/(1-z), z, 2*n+1);
%p A212234  coeff(S,z,2*n);
%p A212234 end proc:
%p A212234 map(f, [$1..50]); # _Robert Israel_, Mar 06 2018
%K A212234 nonn
%O A212234 1,1
%A A212234 _R. H. Hardin_ May 06 2012