

A020942


First column of 3rdorder Zeckendorf array.


6



1, 5, 7, 10, 14, 18, 20, 24, 26, 29, 33, 35, 38, 42, 46, 48, 51, 55, 59, 61, 65, 67, 70, 74, 78, 80, 84, 86, 89, 93, 95, 98, 102, 106, 108, 112, 114, 117, 121, 123, 126, 130, 134, 136, 139, 143, 147, 149, 153, 155, 158, 162, 164, 167, 171, 175, 177, 180, 184
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OFFSET

1,2


COMMENTS

I would like to get similar sequences where the least term in the representation is 2 [ gives 2 8 11 15 21 27 30... ], 3, 4, 6, etc. They are the 2nd, 3rd, etc. columns of the 3rdorder Zeckendorf array.


LINKS

Table of n, a(n) for n=1..59.
Larry Ericksen and Peter G. Anderson, Patterns in differences between rows in kZeckendorf arrays, The Fibonacci Quarterly, Vol. 50, February 2012.  N. J. A. Sloane, Jun 10 2012
C. Kimberling, The Zeckendorf array equals the Wythoff array, Fibonacci Quarterly 33 (1995) 38.


FORMULA

Any number n has unique representation as a sum of terms from {1, 2, 3, 4, 6, 9, 13, 19, ...} (cf. A000930) such that no two terms are adjacent or penadjacent; e.g., 7=6+1. Sequence gives all n where that representation involves 1.
Conjecture: a(n) = A202342(n) + n.  Sean A. Irvine, May 05 2019


EXAMPLE

1=1; 5=4+1; 7=6+1; 10=9+1; etc.


CROSSREFS

Sequence in context: A282107 A022441 A156243 * A190035 A071911 A070875
Adjacent sequences: A020939 A020940 A020941 * A020943 A020944 A020945


KEYWORD

nonn,easy,nice


AUTHOR

Clark Kimberling


EXTENSIONS

More terms from Naohiro Nomoto, Sep 17 2001


STATUS

approved



