A181886 Lower Beatty array of the golden ratio, (1+sqrt(5))/2.

0, 1, 0, 5, 3, 0, 22, 15, 4, 0, 94, 66, 21, 6, 0, 399, 282, 92, 31, 8, 0, 1691, 1197, 393, 137, 41, 9, 0, 7164, 5073, 1668, 586, 181, 47, 11, 0, 30348, 21492, 7069, 2488, 773, 208, 57, 12, 0, 128557, 91044

Offset: 1

Author

Clark Kimberling, Nov 19 2010

Keywords

• nonn
• tabl

Comments

Upper and lower Beatty arrays are defined at A181661.

(row 1)=A049652.

(column 1)=A000004.

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

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

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

whereas column 4 of the upper Beatty array is

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

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

Examples

			Northwest corner of the array:
0....1....5....22....94....399...
0....3...15....66...282...1197...
0....4...21....92...393...1668...
0....6...31...137...586...2488...
		

Crossrefs

Cf. A181661, A000201, A001950, A000045.