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A185736 Weight array of the Wythoff array, by antidiagonals. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 A085247 A003016

Adjacent sequences:  A185733 A185734 A185735 * A185737 A185738 A185739

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 02 2011

STATUS

approved

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Last modified March 18 19:58 EDT 2019. Contains 321293 sequences. (Running on oeis4.)