A166238 Horizontal para-Narayana sequence: says which column of 3rd-order Zeckendorf array (starting column count at 0) contains n.

0, 1, 2, 3, 0, 4, 0, 1, 5, 0, 1, 2, 6, 0, 1, 2, 3, 0, 7, 0, 1, 2, 3, 0, 4, 0, 1, 8, 0, 1, 2, 3, 0, 4, 0, 1, 5, 0, 1, 2, 9, 0, 1, 2, 3, 0, 4, 0, 1, 5, 0, 1, 2, 6, 0, 1, 2, 3, 0, 10, 0, 1, 2, 3, 0, 4, 0, 1, 5, 0, 1, 2, 6, 0, 1, 2, 3, 0, 7, 0, 1, 2, 3, 0, 4, 0, 1, 11, 0, 1, 2, 3, 0, 4, 0, 1, 5, 0, 1, 2, 6, 0, 1, 2, 3

Offset

1,3

Comments

This sequence has the same relationship to A000930 (the Narayana's Cows sequence) as A035614 has to the Fibonacci numbers. Consequently, just as A035614 is the number of initial consecutive zeros in the Fibonacci coding of n (A014417), a(n) is the number of initial consecutive zeros in the analogous coding of n that uses the Narayana sequence as its base.

Links

Table of n, a(n) for n=1..105.

Formula

The segment between the first M and the first M+1 is given by the segment before the first M-2.

Example

The upper-left corner of the 3rd-order Zeckendorf array (A136189) is as follows:
1   2   3   4   6
5   8  12  17  25
7  11  16  23  34
a(1) = a(5) = a(7) = 0, because 1, 5, and 7 occur in column 0;
a(2) = a(8) = a(11) = 1, because 2, 8, and 11 occur in column 1, etc.

Prog

(Haskell)
a166238 = a' 0 where a' n = n : takeWhile (< (n - 2)) a166238 ++ a' (n + 1)
-- Ryan Hendrickson, Jun 17 2015

Crossrefs

Cf. A035614, A136189.

Sequence in context: A122059 A324906 A164917 * A293275 A014197 A341825

Adjacent sequences: A166235 A166236 A166237 * A166239 A166240 A166241

Keyword

easy,nonn

Author

Ryan Hendrickson, Oct 09 2009

Status

approved