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A362829 Positions in lexicographic order of odd partitions of sufficiently large numbers.

%I A362829 #61 Sep 18 2023 06:18:08
%S A362829 1,3,7,10,15,20,27,30,39,41,51,56,69,72,75,93,95,101,123,128,132,134,
%T A362829 160,163,166,172,176,212,214,220,227,229,273,278,282,284,291,297,353,
%U A362829 356,359,365,369,379,382,384,453,455,461,468,470,481,483,490,579,584
%N A362829 Positions in lexicographic order of odd partitions of sufficiently large numbers.
%C A362829 a(n) is the position in lexicographic order of the n-th odd partition of a sufficiently large number k. As long as the number k whose partitions we are examining is large enough, a(n) will exist and won't change for different k. The number of partitions of an odd number, for example, 101 for k=13, will always appear in the sequence, since 13 is the 101st partition in lexicographic order.
%C A362829 Equivalently, positions of partitions with all parts odd among all partitions with no parts of size 1, ordered first by sum, then lexicographically (with the parts in nondecreasing order); or positions of partitions with all parts even among all partitions ordered first by the number of parts plus the sum of the parts, then lexicographically. - _Pontus von Brömssen_, Sep 14 2023
%H A362829 Pontus von Brömssen, <a href="/A362829/b362829.txt">Table of n, a(n) for n = 1..10000</a>
%e A362829 a(1)=1 because 1+1+...+1 (k times) is the first partition in lexicographic order of any positive integer k, and it is odd.
%e A362829 a(2)=3 because 1+1+...+1(k-3 times)+3=k is the third partition of k lexicographically and it is odd.
%Y A362829 Cf. A000009, A087897, A000041.
%K A362829 nonn
%O A362829 1,2
%A A362829 _Richard Peterson_, Aug 01 2023
%E A362829 More terms from _Pontus von Brömssen_, Sep 14 2023