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A371265 Irregular triangle T(n, k), n >= 0, read by rows; the n-th row lists the numbers m such that A371263(m) = n.

%I A371265 #15 Apr 01 2024 12:09:49
%S A371265 0,1,2,3,4,5,9,6,7,8,10,11,12,13,14,27,15,16,26,28,17,19,20,21,24,25,
%T A371265 29,30,18,22,23,31,32,36,33,34,35,37,38,39,40,41,81,42,43,80,82,44,46,
%U A371265 47,48,78,79,83,84,45,49,77,85,50,58,59,63,72,76,86,90
%N A371265 Irregular triangle T(n, k), n >= 0, read by rows; the n-th row lists the numbers m such that A371263(m) = n.
%C A371265 Row 0 has 1 term; for n > 0, row n has A225081(n-1) terms.
%C A371265 As a flat sequence, this is a permutation of the nonnegative integers, with inverse A371266.
%H A371265 Rémy Sigrist, <a href="/A371265/b371265.txt">Table of n, a(n) for n = 0..9841</a>
%H A371265 Rémy Sigrist, <a href="/A371265/a371265.gp.txt">PARI program</a>
%H A371265 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A371265 Triangle T(n, k) begins:
%e A371265   n   n-th row
%e A371265   --  ------------------------------
%e A371265    0  0
%e A371265    1  1
%e A371265    2  2, 3
%e A371265    3  4
%e A371265    4  5, 9
%e A371265    5  6, 7, 8, 10
%e A371265    6  11, 12
%e A371265    7  13
%e A371265    8  14, 27
%e A371265    9  15, 16, 26, 28
%e A371265   10  17, 19, 20, 21, 24, 25, 29, 30
%e A371265   11  18, 22, 23, 31
%e A371265   12  32, 36
%e A371265   13  33, 34, 35, 37
%e A371265   14  38, 39
%e A371265   15  40
%e A371265 .
%e A371265 Triangle T(n, k) begins, in balanced ternary, with row indexes in binary:
%e A371265   bin(n)  n-th row in balanced ternary
%e A371265   ------  ----------------------------------------------
%e A371265        0  0
%e A371265        1  1
%e A371265       10  1T, 10
%e A371265       11  11
%e A371265      100  1TT, 100
%e A371265      101  1T0, 1T1, 10T, 101
%e A371265      110  11T, 110
%e A371265      111  111
%e A371265     1000  1TTT, 1000
%e A371265     1001  1TT0, 1TT1, 100T, 1001
%e A371265     1010  1T0T, 1T01, 1T1T, 1T10, 10T0, 10T1, 101T, 1010
%e A371265     1011  1T00, 1T11, 10TT, 1011
%e A371265     1100  11TT, 1100
%e A371265     1101  11T0, 11T1, 110T, 1101
%e A371265     1110  111T, 1110
%e A371265     1111  1111
%o A371265 (PARI) \\ See Links section.
%Y A371265 See A371257 for a similar sequence.
%Y A371265 Cf. A225081, A371266 (inverse).
%K A371265 nonn,base,tabf
%O A371265 0,3
%A A371265 _Rémy Sigrist_, Mar 16 2024