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Number of partitions of 2*n+1 into three parts from A339506.
0

%I #10 Apr 01 2021 15:16:24

%S 0,1,1,2,3,3,3,4,3,4,4,4,3,4,2,3,3,3,5,5,5,5,6,6,9,9,8,8,7,5,8,5,8,7,

%T 7,6,7,6,8,8,7,9,7,7,8,7,6,8,6,6,6,5,6,9,8,12,10,9,9,8,8,8,9,7,7,5,6,

%U 6,8,9,10,8

%N Number of partitions of 2*n+1 into three parts from A339506.

%C Conjecture: for n > 0 this sequence is always positive (it has been verified up to 10^6).

%e a(0) = 0 because 2*0+1 = 1 is not the sum of 3 terms of A339506.

%e a(1) = 1 because 2*1+1 = 3 and 3 = 1+1+1 (1 is the term of A339506).

%e a(2) = 1 because 2*2+1 = 5 and 5 = 1+1+3 (1 and 3 are terms of A339506).

%e a(3) = 2 because 2*3+1 = 7 and 7 = 1+1+5 = 1+3+3 (1, 3, 5 are terms of A339506).

%e a(4) = 3 because 2*4+1 = 9 and 9 = 1+1+7 = 1+3+5 = 3+3+3 (1, 3, 5, 7 are terms of A339506).

%Y Cf. A190353, A249876, A339506.

%K nonn

%O 0,4

%A _Lechoslaw Ratajczak_, Feb 22 2021