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

2,1

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.)

Links

Table of n, a(n) for n=2..67.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A259556, A259601.

Sequence in context: A004221 A239504 A033557 * A088298 A075992 A022294

Adjacent sequences: A259597 A259598 A259599 * A259601 A259602 A259603

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Jul 22 2015

Status

approved