

A134563


Array read by antidiagonals: row n consists of numbers whose 3rdorder Zeckendorf representation has exactly n terms.


2



1, 2, 5, 3, 7, 18, 4, 8, 24, 59, 6, 10, 26, 78, 188, 9, 11, 27, 84, 248, 594, 13, 12, 33, 86, 267, 783, 1872, 19, 14, 35, 87, 273, 843
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OFFSET

1,2


COMMENTS

A permutation of the natural numbers.


LINKS

Table of n, a(n) for n=1..34.
C. Kimberling, The Zeckendorf array equals the Wythoff array, Fibonacci Quarterly 33 (1995) 38.
Index entries for sequences that are permutations of the natural numbers


FORMULA

Row 1, A000930, is the 3rdorder Zeckendorf basis, b(1), b(2), b(3), .... Every positive integer has a unique 3rdorder Zeckendorf representation b(i(1)) + b(i(2)) + ... + b(i(n)), where i(h)  i(j) >=3 for distinct h and j.


EXAMPLE

Northwest corner of the array:
1 2 3 4 6 9 13 19 28 41 60 88 129 ...
5 7 8 10 11 12 ...
18 24 26 27 33 35 ...
59 78 84 86 87 106 ...
For example, 26=19+6+1 has 3 terms, so 26 is in row 3.


CROSSREFS

Cf. A000930, A136189, A134564.
Sequence in context: A084334 A096878 A249162 * A192178 A201914 A331217
Adjacent sequences: A134560 A134561 A134562 * A134564 A134565 A134566


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Nov 01 2007, Dec 18 2007


STATUS

approved



