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A191360 Number of the diagonal of the Wythoff array that contains n. 3
0, 1, 2, -1, 3, -2, 0, 4, -3, -1, 1, -4, 5, -5, -2, 0, -6, 2, -7, -3, 6, -8, -4, -1, -9, 1, -10, -5, 3, -11, -6, -2, -12, 7, -13, -7, -3, -14, 0, -15, -8, 2, -16, -9, -4, -17, 4, -18, -10, -5, -19, -1, -20, -11, 8, -21, -12, -6, -22, -2, -23, -13, 1, -24, -14, -7, -25, 3, -26, -15, -8, -27, -3, -28, -16, 5, -29, -17, -9, -30 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Every integer occurs in A191360 (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.

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

The main diagonal of the Wythoff array is (1,7,16,...); that's diagonal #0, so that a(1)=0, a(7)=0, a(16)=0.

MATHEMATICA

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

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

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

(* t=A035513, the Wythoff array *)

a = Flatten[Table[If[g[i, j] == n, j - i, {}], {n, 80}, {i, 40}, {j, 40}]]

(* a=A191360 *)

CROSSREFS

Cf. A035513, A114327, A191361, A191362.

Sequence in context: A325178 A190451 A282743 * A144029 A166949 A114890

Adjacent sequences:  A191357 A191358 A191359 * A191361 A191362 A191363

KEYWORD

sign

AUTHOR

Clark Kimberling, May 31 2011

STATUS

approved

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Last modified October 17 13:57 EDT 2019. Contains 328113 sequences. (Running on oeis4.)