|
%I #14 Nov 27 2019 02:36:58
%S 1,1,1,2,1,2,1,2,2,2,2,2,2,2,2,3,2,3,2,3,2,3,2,3,3,3,3,3,3,3,3,3,3,3,
%T 3,4,3,4,3,4,3,4,3,4,3,4,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,4,5,4,5,
%U 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
%N a(n) = number of partitions of n into a pair of parts n=p+q, p>=q>=0, with p-q equal to a square >= 0.
%C Number of integers k, 0 <= 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 f := n->if n mod 2 = 0 then floor(sqrt((n-2)/4))+1 else floor(sqrt((n-2)/4)-1/2)+1; fi; # then add 1 if n is a square!
%o (PARI)
%o a(n)={my(ct=0,d=0); while(d^2<=n, if((n-d^2)%2==0, ct+=1); d+=1 ); return(ct); }
%o /* _Joerg Arndt_, Oct 08 2012 */
%Y See A084359 for another version.
%K nonn,easy
%O 1,4
%A Anne M. Donovan (anned3005(AT)aol.com), May 31 2003
%E More terms from _Michel ten Voorde_, Jun 13 2003
|
