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A097305 Array of number of partitions of n with odd parts only and largest part 2*m-1 with m in {1,2,..., ceiling(n/2)}.

%I A097305 #11 Aug 29 2019 16:07:17
%S A097305 1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,2,2,1,1,3,2,1,1,1,3,3,2,1,1,3,4,2,
%T A097305 1,1,1,4,4,3,2,1,1,4,5,4,2,1,1,1,4,6,5,3,2,1,1,5,7,6,4,2,1,1,1,5,8,7,
%U A097305 5,3,2,1,1,5,9,9,6,4,2,1,1,1,6,10,10,8,5,3,2,1,1,6,11,12,10,6,4,2,1,1,1,6
%N A097305 Array of number of partitions of n with odd parts only and largest part 2*m-1 with m in {1,2,..., ceiling(n/2)}.
%C A097305 The sequence of row lengths of this array is A008619 = [1,1,2,2,3,3,4,4,5,5,6,6,7,7,...].
%C A097305 This is the first difference array of A097306.
%C A097305 The number of partitions of N=2*n (n>=1) into even parts with largest part 2*k, with k from 1,..,n, is given by the triangle A008284(n,k).
%H A097305 W. Lang, <a href="/A097305/a097305.txt">First 18 rows</a>.
%F A097305 T(n, m)= number of partitions of n with only odd parts and largest part is k:=2*m-1, m=1, 2, ..., ceiling(n/2).
%e A097305 [1]; [1]; [1,1]; [1,1]; [1,1,1]; [1,2,1]; [1,2,1,1]; [1,2,2,1]; ...
%e A097305 T(8,2)=2 because there are two partitions of 8 with odd parts from {1,3} and 3 appears at least once, namely (1^5,3) and (1^2,3^2).
%e A097305 T(6,2)=2 from 6= 3+3 = 1+1+1+3.
%Y A097305 Row sums: A000009.
%K A097305 nonn,tabf,easy
%O A097305 1,11
%A A097305 _Wolfdieter Lang_, Aug 13 2004