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.

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, 5

Offset

1,6

Comments

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

Links

Table of n, a(n) for n=1..105.

Formula

See Maple line.

Example

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

Maple

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

Crossrefs

See A083023 for another version.

Sequence in context: A198333 A191591 A083023 * A143935 A008616 A331973

Adjacent sequences: A084356 A084357 A084358 * A084360 A084361 A084362

Keyword

nonn

Author

Amarnath Murthy, May 27 2003

Status

approved