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

2,1

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.)

Links

Table of n, a(n) for n=2..66.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000045, A001950, A259556, A259600.

Sequence in context: A023180 A029474 A302134 * A351041 A075335 A250220

Adjacent sequences: A259598 A259599 A259600 * A259602 A259603 A259604

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Jul 22 2015

Status

approved