A259601 Triangular array: sums of two distinct upper Wythoff numbers.

7, 9, 12, 12, 15, 17, 15, 18, 20, 23, 17, 20, 22, 25, 28, 20, 23, 25, 28, 31, 33, 22, 25, 27, 30, 33, 35, 38, 25, 28, 30, 33, 36, 38, 41, 43, 28, 31, 33, 36, 39, 41, 44, 46, 49, 30, 33, 35, 38, 41, 43, 46, 48, 51, 54, 33, 36, 38, 41, 44, 46, 49, 51, 54, 57

Offset: 2

Author

Clark Kimberling, Jul 22 2015

Keywords

• nonn
• tabl
• easy

Comments

Row n shows the numbers v(m) + v(n), where v = A001950 (upper 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

			17 = 7 + 10 = v(3) + v(4), so that 17 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:
7
9    12
12   15   17
15   18   20   23
17   20   22   25   28
20   23   25   28   31   33
22   25   27   30   33   35   38
25   28   30   33   36   38   41   43
		

Crossrefs

Cf. A000045, A001950, A259556, A259600.

Programs

Mathematica

r = GoldenRatio; z = 13; v[n_] := v[n] = Floor[n*r^2];
s[m_, n_] := v[m] + v[n]; t = Table[s[m, n], {n, 2, z}, {m, 1, n - 1}]
TableForm[t] (* A259601 array *)
Flatten[t]   (* A259601 sequence *)

PARI

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