A371590 - OEIS

A371590

Irregular table T(n, k), n >= 0, k = 1..max(2, 2^n), read by rows; the n-th row lists the nonnegative numbers whose Zeckendorf-binary representation has n nonleading zeros.

%I #10 Apr 14 2024 10:04:21

%S 0,1,2,4,3,6,7,12,5,9,10,11,17,19,20,33,8,14,15,16,18,25,27,28,30,31,

%T 32,46,51,53,54,88,13,22,23,24,26,29,38,40,41,43,44,45,48,49,50,52,67,

%U 72,74,75,80,82,83,85,86,87,122,135,140,142,143,232

%N Irregular table T(n, k), n >= 0, k = 1..max(2, 2^n), read by rows; the n-th row lists the nonnegative numbers whose Zeckendorf-binary representation has n nonleading zeros.

%C As a flat sequence, this is a permutation of the nonnegative integers with inverse A371591.

%H Rémy Sigrist, <a href="/A371590/a371590.gp.txt">PARI program</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F A102364(T(n, k)) = n.

%F T(n, 1) = A000045(n + 2) for any n > 0.

%F T(n, max(2, 2^n)) = A027941(n + 1) for any n >= 0.

%e Array T(n, k) begins:

%e 0, 1

%e 2, 4

%e 3, 6, 7, 12

%e 5, 9, 10, 11, 17, 19, 20, 33

%e 8, 14, 15, 16, 18, 25, 27, 28, 30, 31, 32, 46, 51, 53, 54, 88

%e ...

%o (PARI) \\ See Links section.

%Y See A371592 for a similar sequence.

%Y Cf. A000045, A027941, A102364, A371591 (inverse).

%K nonn,base,tabf

%O 0,3

%A _Rémy Sigrist_, Mar 28 2024