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A083023 a(n) = number of partitions of n into 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

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: 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 June 16 11:47 EDT 2019. Contains 324152 sequences. (Running on oeis4.)