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 A083023 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. 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Number of integers k, 0 <= k <= n/2 such that n - 2k is a square. LINKS FORMULA See Maple line. EXAMPLE a(11) = 2: the partitions are (1,10) and (5,6). MAPLE 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! PROG (PARI) a(n)={my(ct=0, d=0); while(d^2<=n, if((n-d^2)%2==0, ct+=1); d+=1 ); return(ct); } /* Joerg Arndt, Oct 08 2012 */ CROSSREFS See A084359 for another version. Sequence in context: A085035 A198333 A191591 * A084359 A143935 A008616 Adjacent sequences:  A083020 A083021 A083022 * A083024 A083025 A083026 KEYWORD nonn,easy AUTHOR Anne M. Donovan (anned3005(AT)aol.com), May 31 2003 EXTENSIONS More terms from Michel ten Voorde, Jun 13 2003 STATUS approved

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Last modified September 20 19:48 EDT 2020. Contains 337265 sequences. (Running on oeis4.)