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%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
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