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%I #24 Jun 17 2015 09:47:07
%S 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,
%T 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,
%U 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
%N Horizontal para-Narayana sequence: says which column of 3rd-order Zeckendorf array (starting column count at 0) contains n.
%C 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.
%F The segment between the first M and the first M+1 is given by the segment before the first M-2.
%e The upper-left corner of the 3rd-order Zeckendorf array (A136189) is as follows:
%e 1 2 3 4 6
%e 5 8 12 17 25
%e 7 11 16 23 34
%e a(1) = a(5) = a(7) = 0, because 1, 5, and 7 occur in column 0;
%e a(2) = a(8) = a(11) = 1, because 2, 8, and 11 occur in column 1, etc.
%o (Haskell)
%o a166238 = a' 0 where a' n = n : takeWhile (< (n - 2)) a166238 ++ a' (n + 1)
%o -- _Ryan Hendrickson_, Jun 17 2015
%Y Cf. A035614, A136189.
%K easy,nonn
%O 1,3
%A _Ryan Hendrickson_, Oct 09 2009
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