cp's OEIS Frontend

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

%I A272020 #24 Nov 27 2024 08:00:27
%S A272020 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,
%T A272020 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,
%U A272020 4,3,1,5,4,3,2,5,4,3,2,1,6,6,1,6,2,6,2,1
%N A272020 Irregular triangle read by rows: strictly decreasing sequences of positive numbers given in lexicographic order.
%C A272020 Length of n-th row given by A000120(n);
%C A272020 Min of n-th row given by A001511(n);
%C A272020 Sum of n-th row given by A029931(n);
%C A272020 Product of n-th row given by A096111(n);
%C A272020 Max of n-th row given by A113473(n);
%C A272020 Numerator of sum of reciprocals of n-th row given by A116416(n);
%C A272020 Denominator of sum of reciprocals of n-th row given by A116417(n);
%C A272020 LCM of n-th row given by A271410(n).
%C A272020 The first appearance of n is at A001787(n - 1).
%C A272020 n-th row begins at index A000788(n - 1) for n > 0.
%C A272020 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
%H A272020 Peter Kagey, <a href="/A272020/b272020.txt">Table of n, a(n) for n = 0..10000</a>
%e A272020 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.
%e A272020 Row 0: []
%e A272020 Row 1: [1]
%e A272020 Row 2: [2]
%e A272020 Row 3: [2, 1]
%e A272020 Row 4: [3]
%e A272020 Row 5: [3, 1]
%e A272020 Row 6: [3, 2]
%e A272020 Row 7: [3, 2, 1]
%p A272020 T:= proc(n) local i, l, m; l:= NULL; m:= n;
%p A272020       if n=0 then return [][] fi; for i while m>0 do
%p A272020       if irem(m, 2, 'm')=1 then l:=i, l fi od; l
%p A272020     end:
%p A272020 seq(T(n), n=0..35);  # _Alois P. Heinz_, Nov 27 2024
%t A272020 Table[Reverse[Join@@Position[Reverse[IntegerDigits[n,2]],1]],{n,0,100}] (* _Gus Wiseman_, Jan 17 2023 *)
%Y A272020 Cf. A000120, A096111, A116416, A116417, A271410, A001787.
%Y A272020 Cf. A048793 gives the rows in reverse order.
%Y A272020 Cf. A272011.
%Y A272020 Lasts are A001511.
%Y A272020 Heinz numbers of the rows are A019565.
%Y A272020 Firsts are A029837 or A070939 or A113473.
%Y A272020 Row sums are A029931.
%Y A272020 A066099 lists standard comps, partial sums A358134, weighted sum A359042.
%Y A272020 Cf. A005940, A059893, A125106, A161511, A242628.
%K A272020 nonn,tabf
%O A272020 0,2
%A A272020 _Peter Kagey_, Apr 17 2016