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A166238 Horizontal para-Narayana sequence: says which column of 3rd-order Zeckendorf array (starting column count at 0) contains n. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A122059 A324906 A164917 * A293275 A014197 A341825
KEYWORD
easy,nonn
AUTHOR
Ryan Hendrickson, Oct 09 2009
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)