A259600 Triangular array: sums of two distinct lower Wythoff numbers.

4, 5, 7, 7, 9, 10, 9, 11, 12, 14, 10, 12, 13, 15, 17, 12, 14, 15, 17, 19, 20, 13, 15, 16, 18, 20, 21, 23, 15, 17, 18, 20, 22, 23, 25, 26, 17, 19, 20, 22, 24, 25, 27, 28, 30, 18, 20, 21, 23, 25, 26, 28, 29, 31, 33, 20, 22, 23, 25, 27, 28, 30, 31, 33, 35, 36

Offset: 2

Author

Clark Kimberling, Jul 22 2015

Keywords

• nonn
• tabl
• easy

Comments

Row n shows the numbers u(m) + u(n), where u = A000201 (lower Wythoff sequence), for m=1..n-1, for n >= 2. (The offset is 2, so that the top row is counted as row 2.)

Examples

			10 = 4 + 6 = u(3) + u(4), so that 10 appears as the final term in row 4. (The offset is 2, so that the top row is counted as row 2.) Rows 2 to 9:
4
5    7
7    9    10
9    11   12   14
10   12   13   15   17
12   14   15   17   19   20
13   15   16   18   20   21   23
15   17   18   20   22   23   25   26
		

Crossrefs

Cf. A259556, A259601.

Programs

Mathematica

r = GoldenRatio; z = 20; u[n_] := u[n] = Floor[n*r];
s[m_, n_] := u[m] + u[n]; t = Table[s[m, n], {n, 2, z}, {m, 1, n - 1}];
TableForm[t]  (* A259600 array *)
Flatten[t]  (* A259600 sequence *)

PARI

tabl(nn) = {r=(sqrt(5)+1)/2; for (n=2, nn, for (k=1, n-1, print1(floor(n*r) + floor(k*r), ", ");); print(););} \\ Michel Marcus, Jul 30 2015