A181886 - OEIS

%I #4 Mar 30 2012 18:57:11

%S 0,1,0,5,3,0,22,15,4,0,94,66,21,6,0,399,282,92,31,8,0,1691,1197,393,

%T 137,41,9,0,7164,5073,1668,586,181,47,11,0,30348,21492,7069,2488,773,

%U 208,57,12,0,128557,91044

%N Lower Beatty array of the golden ratio, (1+sqrt(5))/2.

%C Upper and lower Beatty arrays are defined at A181661.

%C (row 1)=A049652.

%C (column 1)=A000004.

%C (column 2)=A000201 (lower Wythoff sequence).

%C (column 3)=u(l(n))+l(u(n)), or simply ul+lu.

%C (column 4)=u(ul+lu)+l(uu+ll),

%C whereas column 4 of the upper Beatty array is

%C u(uu+ll)+l(ul+lu).

%C U(n,k)-L(n,k)=n for n>=1, k>=0.

%e Northwest corner of the array:

%e 0....1....5....22....94....399...

%e 0....3...15....66...282...1197...

%e 0....4...21....92...393...1668...

%e 0....6...31...137...586...2488...

%Y Cf. A181661, A000201, A001950, A000045.

%K nonn,tabl

%O 1,4

%A _Clark Kimberling_, Nov 19 2010