A185736 Weight array of the Wythoff array, by antidiagonals.

1, 1, 3, 1, 2, 2, 2, 3, 1, 3, 3, 5, 2, 2, 3, 5, 8, 3, 3, 2, 2, 8, 13, 5, 5, 3, 1, 3, 13, 21, 8, 8, 5, 2, 2, 2, 21, 34, 13, 13, 8, 3, 3, 1, 3, 34, 55, 21, 21, 13, 5, 5, 2, 2, 3, 55, 89, 34, 34, 21, 8, 8, 3, 3, 2, 2, 89, 144, 55, 55, 34, 13, 13, 5, 5, 3, 1, 3, 144, 233, 89, 89, 55, 21, 21, 8, 8, 5, 2, 2, 3, 233, 377, 144, 144, 89, 34, 34, 13, 13, 8, 3, 3, 2, 2, 377, 610, 233, 233, 144, 55, 55, 21, 21, 13, 5, 5, 3, 1

Offset

1,3

Comments

The Wythoff array, A035513, is the accumulation array of A185736. These arrays chain:

... ->A185736->A035513->A185737-> ... (For definitions of weight array and accumulation array, see A144112.)Every term of A185736 is a Fibonacci number.

Links

Table of n, a(n) for n=1..119.

Formula

Row 1: 1 0 0 1 1 2 (continue with Fibonacci recurrence)

Row 2: 3 2 3 5 8 13 (continue with Fib. recurrence)

Row 3: 2 1 2 3 5 8 (continue with Fib. recurrence)

For m>3, if the row number is m of form floor(h*r+1), where r=(1+sqrt(5))/2, then (row m)=(row 2); otherwise, (row m)=(row 3).

Example

Northwest corner:
1 1 1 2 3 4 8
3 2 3 5 8 13 21
2 1 2 3 5 8 13
3 2 3 5 8 13 21
3 2 3 5 8 13 21
2 1 2 3 5 8 13

Crossrefs

Cf. A035513, A185737.

Sequence in context: A291047 A033178 A029418 * A144148 A343950 A085247

Adjacent sequences: A185733 A185734 A185735 * A185737 A185738 A185739

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 02 2011

Status

approved