|
%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
|
