A259601 - OEIS

%I #17 Jul 31 2015 04:28:53

%S 7,9,12,12,15,17,15,18,20,23,17,20,22,25,28,20,23,25,28,31,33,22,25,

%T 27,30,33,35,38,25,28,30,33,36,38,41,43,28,31,33,36,39,41,44,46,49,30,

%U 33,35,38,41,43,46,48,51,54,33,36,38,41,44,46,49,51,54,57

%N Triangular array: sums of two distinct upper Wythoff numbers.

%C 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.)

%e 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:

%e 7

%e 9    12

%e 12   15   17

%e 15   18   20   23

%e 17   20   22   25   28

%e 20   23   25   28   31   33

%e 22   25   27   30   33   35   38

%e 25   28   30   33   36   38   41   43

%t r = GoldenRatio; z = 13; v[n_] := v[n] = Floor[n*r^2];

%t s[m_, n_] := v[m] + v[n]; t = Table[s[m, n], {n, 2, z}, {m, 1, n - 1}]

%t TableForm[t] (* A259601 array *)

%t Flatten[t]   (* A259601 sequence *)

%o (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

%Y Cf. A000045, A001950, A259556, A259600.

%K nonn,tabl,easy

%O 2,1

%A _Clark Kimberling_, Jul 22 2015