A191361 Number of the diagonal of the Wythoff difference array that contains n.

0, 1, -1, -2, 2, -3, 0, -4, -5, -1, -6, -7, 3, -8, -2, -9, -10, 1, -11, -3, -12, -13, -4, -14, -15, 0, -16, -5, -17, -18, -6, -19, -20, 4, -21, -7, -22, -23, -1, -24, -8, -25, -26, -9, -27, -28, 2, -29, -10, -30, -31, -2, -32, -11, -33, -34, -12, -35, -36, -3

Offset: 1

Author

Clark Kimberling, May 31 2011

Keywords

• sign

Comments

Every integer occurs in A191361 (infinitely many times).

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;

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

Examples

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

Crossrefs

Cf. A080164, A114327, A191360, A191362.

Programs

Mathematica

r = GoldenRatio; f[n_] := Fibonacci[n];
g[i_, j_] := f[2 j - 1]*Floor[i*r] + (i - 1) f[2 j - 2];
TableForm[Table[g[i, j], {i, 1, 10}, {j, 1, 5}]]
(* A080164, Wythoff difference array *)
a = Flatten[Table[If[g[i, j] == n, j - i, {}], {n, 60}, {i, 50}, {j, 50}]]
(* a=A191361 *)