%I A119462
%S A119462 1,2,2,2,2,6,2,12,2,2,20,10,2,30,30,2,2,42,70,14,2,56,140,56,2,2,72,252,
%T A119462 168,18,2,90,420,420,90,2,2,110,660,924,330,22,2,132,990,1848,990,132,
               2,
%U A119462 2,156,1430,3432,2574,572,26,2,182,2002,6006,6006,2002,182,2,2,210,2730
%N A119462 Triangle read by rows: T(n,k) is the number of circular binary words 
               of length n having k occurrences of 01 (0<=k<=floor(n/2)).
%C A119462 Row n contains 1+floor(n/2) terms. Sum of entries in row n is 2^n (A000079). 
               T(n,0)=2 for n>=1. T(n,1)=2*binomial(n,2)=A002378(n-1). T(n,2)=2*binomial(n,
               4)=A034827(n). T(n,k)=2*A034239(n-1,k) for n>=1. Sum(k*T(n,k),k=0..floor(n/
               2))=A057711(n).
%D A119462 L. Carlitz and R. Scoville, Zero-one sequences and Fibonacci numbers, 
               Fibonacci Quarterly, 15 (1977), 246-254.
%F A119462 T(n,k)=2*binomial(n,2k) for n>=1; T(0,0)=1. T(n,k)=2T(n-1,k)-T(n-2,k)+T(n-2,
               k-1) for n>=3. G.f.=G(t,z)=(1-z^2+tz^2)/(1-2z+z^2-tz^2).
%e A119462 T(3,1)=6 because we have 001,010,011,100,101 and 110.
%e A119462 Triangle starts:
%e A119462 1;
%e A119462 2;
%e A119462 2,2;
%e A119462 2,6;
%e A119462 2,12,2;
%e A119462 2,20,10;
%e A119462 2,30,30,2;
%p A119462 T:=proc(n,k) if n=0 and k=0 then 1 else 2*binomial(n,2*k) fi end: for 
               n from 0 to 15 do seq(T(n,k),k=0..floor(n/2)) od; # yields sequence 
               in triangular form
%Y A119462 Cf. A000079, A002378, A034827, A034239, A057711.
%Y A119462 Sequence in context: A163368 A151948 A080400 this_sequence A096625 A103222 
               A061033
%Y A119462 Adjacent sequences: A119459 A119460 A119461 this_sequence A119463 A119464 
               A119465
%K A119462 nonn,tabf
%O A119462 0,2
%A A119462 Emeric Deutsch (deutsch(AT)duke.poly.edu), May 21 2006