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, 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

Offset

1,4

Comments

Number of integers k, 0 <= k <= n/2 such that n - 2k is a square.

Links

Table of n, a(n) for n=1..102.

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: A378122 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