A191361 - OEIS

%I #6 Mar 30 2012 18:57:32

%S 0,1,-1,-2,2,-3,0,-4,-5,-1,-6,-7,3,-8,-2,-9,-10,1,-11,-3,-12,-13,-4,

%T -14,-15,0,-16,-5,-17,-18,-6,-19,-20,4,-21,-7,-22,-23,-1,-24,-8,-25,

%U -26,-9,-27,-28,2,-29,-10,-30,-31,-2,-32,-11,-33,-34,-12,-35,-36,-3

%N Number of the diagonal of the Wythoff difference array that contains n.

%C Every integer occurs in A191361 (infinitely many times).

%C Represent the array as {g(i,j): i>=1, j>=1}.  Then for m>=0, (diagonal #m) is the sequence (g(i,i+m)), i>=1;

%C for m<0, (diagonal #m) is the sequence (g(i+m,i)), i>=1.

%e Diagonal #0 (the main diagonal) of A080164 is (1,7,26,...), so a(1)=0, a(7)=0, a(26)=0.

%t r = GoldenRatio; f[n_] := Fibonacci[n];

%t g[i_, j_] := f[2 j - 1]*Floor[i*r] + (i - 1) f[2 j - 2];

%t TableForm[Table[g[i, j], {i, 1, 10}, {j, 1, 5}]]

%t (* A080164, Wythoff difference array *)

%t a = Flatten[Table[If[g[i, j] == n, j - i, {}], {n, 60}, {i, 50}, {j, 50}]]

%t (* a=A191361 *)

%Y Cf. A080164, A114327, A191360, A191362.

%K sign

%O 1,4

%A _Clark Kimberling_, May 31 2011