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Irregular triangle T(n, k), n >= 0, k = 1..2^A005811(n), read by rows; the n-th row lists the numbers m such that A371256(m) = n.
5

%I #19 Apr 01 2024 12:08:47

%S 0,1,2,3,5,6,7,4,8,9,17,18,22,10,11,15,16,19,20,21,23,12,14,24,25,13,

%T 26,27,53,54,67,28,29,51,52,55,56,66,68,30,32,33,34,46,47,48,50,57,59,

%U 60,61,64,65,69,70,31,35,45,49,58,62,63,71,36,44,72,76

%N Irregular triangle T(n, k), n >= 0, k = 1..2^A005811(n), read by rows; the n-th row lists the numbers m such that A371256(m) = n.

%C The n-th row has 2^A005811(n) terms.

%C As a flat sequence, this is a permutation of the nonnegative integers, with inverse A371258.

%H Rémy Sigrist, <a href="/A371257/b371257.txt">Table of n, a(n) for n = 0..6560</a>

%H Rémy Sigrist, <a href="/A371257/a371257.gp.txt">PARI program</a>

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

%e Triangle T(n, k) begins:

%e n n-th row

%e -- --------------------------------------------------------------

%e 0 0

%e 1 1, 2

%e 2 3, 5, 6, 7

%e 3 4, 8

%e 4 9, 17, 18, 22

%e 5 10, 11, 15, 16, 19, 20, 21, 23

%e 6 12, 14, 24, 25

%e 7 13, 26

%e 8 27, 53, 54, 67

%e 9 28, 29, 51, 52, 55, 56, 66, 68

%e 10 30, 32, 33, 34, 46, 47, 48, 50, 57, 59, 60, 61, 64, 65, 69, 70

%e 11 31, 35, 45, 49, 58, 62, 63, 71

%e 12 36, 44, 72, 76

%e 13 37, 38, 42, 43, 73, 74, 75, 77

%e 14 39, 41, 78, 79

%e 15 40, 80

%e .

%e Triangle T(n, k) begins, in ternary, with row indexes in binary:

%e bin(n) n-th row in ternary

%e ------ ----------------------------------------------

%e 0 0

%e 1 1, 2

%e 10 10, 12, 20, 21

%e 11 11, 22

%e 100 100, 122, 200, 211

%e 101 101, 102, 120, 121, 201, 202, 210, 212

%e 110 110, 112, 220, 221

%e 111 111, 222

%e 1000 1000, 1222, 2000, 2111

%e 1001 1001, 1002, 1220, 1221, 2001, 2002, 2110, 2112

%o (PARI) \\ See Links section.

%Y See A371265 for a similar sequence.

%Y Cf. A005811, A166242, A368229, A371256.

%K nonn,base,tabf

%O 0,3

%A _Rémy Sigrist_, Mar 16 2024