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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 05:20 EDT 2021. Contains 347609 sequences. (Running on oeis4.)