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A084359 a(n) = number of partitions of n into pair of parts n=p+q, p>=q>=1, with p-q equal to a square >= 0. 2

%I

%S 0,1,1,1,1,2,1,2,1,2,2,2,2,2,2,2,2,3,2,3,2,3,2,3,2,3,3,3,3,3,3,3,3,3,

%T 3,3,3,4,3,4,3,4,3,4,3,4,3,4,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,4,5,

%U 4,5,4,5,4,5,4,5,4,5,4,5,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,5,6,5

%N a(n) = number of partitions of n into pair of parts n=p+q, p>=q>=1, with p-q equal to a square >= 0.

%C Number of integers k, 1 <= k <= n/2 such that n - 2k is a square.

%F See Maple line.

%e a(11) = 2: the partitions are (1,10) and (5,6).

%p A084359 := n->if n mod 2 = 0 then floor(sqrt((n-2)/4))+1 else floor(sqrt((n-2)/4)-1/2)+1; fi; # applies for n >= 2

%Y See A083023 for another version.

%K nonn

%O 1,6

%A _Amarnath Murthy_, May 27 2003

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)