A272020 Irregular triangle read by rows: strictly decreasing sequences of positive numbers given in lexicographic order.

1, 2, 2, 1, 3, 3, 1, 3, 2, 3, 2, 1, 4, 4, 1, 4, 2, 4, 2, 1, 4, 3, 4, 3, 1, 4, 3, 2, 4, 3, 2, 1, 5, 5, 1, 5, 2, 5, 2, 1, 5, 3, 5, 3, 1, 5, 3, 2, 5, 3, 2, 1, 5, 4, 5, 4, 1, 5, 4, 2, 5, 4, 2, 1, 5, 4, 3, 5, 4, 3, 1, 5, 4, 3, 2, 5, 4, 3, 2, 1, 6, 6, 1, 6, 2, 6, 2, 1

Offset

0,2

Comments

Length of n-th row given by A000120(n);

Min of n-th row given by A001511(n);

Sum of n-th row given by A029931(n);

Product of n-th row given by A096111(n);

Max of n-th row given by A113473(n);

Numerator of sum of reciprocals of n-th row given by A116416(n);

Denominator of sum of reciprocals of n-th row given by A116417(n);

LCM of n-th row given by A271410(n).

The first appearance of n is at A001787(n - 1).

n-th row begins at index A000788(n - 1) for n > 0.

Also the reversed positions of 1's in the reversed binary expansion of n. Also the reversed partial sums of the n-th composition in standard order (row n of A066099). Reversing rows gives A048793. - Gus Wiseman, Jan 17 2023

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

Example

Row n is given by the exponents in the binary expansion of 2*n. For example, row 5 = [3, 1] because 2*5 = 2^3 + 2^1.
Row 0: []
Row 1: [1]
Row 2: [2]
Row 3: [2, 1]
Row 4: [3]
Row 5: [3, 1]
Row 6: [3, 2]
Row 7: [3, 2, 1]

Maple

T:= proc(n) local i, l, m; l:= NULL; m:= n;
      if n=0 then return [][] fi; for i while m>0 do
      if irem(m, 2, 'm')=1 then l:=i, l fi od; l
    end:
seq(T(n), n=0..35);  # Alois P. Heinz, Nov 27 2024

Mathematica

Table[Reverse[Join@@Position[Reverse[IntegerDigits[n, 2]], 1]], {n, 0, 100}] (* Gus Wiseman, Jan 17 2023 *)

Crossrefs

Cf. A000120, A096111, A116416, A116417, A271410, A001787.

Cf. A048793 gives the rows in reverse order.

Cf. A272011.

Lasts are A001511.

Heinz numbers of the rows are A019565.

Firsts are A029837 or A070939 or A113473.

Row sums are A029931.

A066099 lists standard comps, partial sums A358134, weighted sum A359042.

Cf. A005940, A059893, A125106, A161511, A242628.

Sequence in context: A212125 A282936 A220073 * A264263 A291123 A292594

Adjacent sequences: A272017 A272018 A272019 * A272021 A272022 A272023

Keyword

nonn,tabf

Author

Peter Kagey, Apr 17 2016

Status

approved