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A061790 Number of sums i^2 + j^2 that occur more than once for 1 <= i <= j <= n. 0
0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 5, 6, 8, 11, 12, 14, 18, 20, 25, 27, 31, 35, 42, 46, 50, 55, 61, 67, 74, 78, 87, 94, 101, 111, 118, 124, 133, 143, 153, 159, 172, 181, 193, 206, 214, 227, 240, 251, 265, 277, 290, 303, 322, 337, 350, 363, 378, 392, 410, 421, 440, 461 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

If the {s+t} sums are generated by addition 2 terms of an S set consisting of n different entries, then at least 1 and at most n(n+1)/2=A000217(n) distinct values can be obtained. The set of first n squares gives results falling between these two extremes.

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

S={1,4,9,...,100,121} provides 61 different sums of two (not necessarily different) squares: {2,5,8,..,202,221,242}. Only 5 of these sums arise more than once:

   50 = 1 +  49 = 25 +  25;

   65 = 1 +  64 = 16 +  49;

   85 = 4 +  81 = 36 +  49;

  125 = 4 + 121 = 25 + 100;

  130 = 9 + 121 = 49 +  81.

Therefore a(11) = (12*11/2) - 61 = 5.

MATHEMATICA

f[x_] := x^2 t0=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}] t1=Table[(w*(w+1)/2)-Part[t0, w], {w, a, b}]

CROSSREFS

Cf. A000217.

Sequence in context: A035938 A024503 A321286 * A107236 A192184 A027586

Adjacent sequences:  A061787 A061788 A061789 * A061791 A061792 A061793

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 22 2001

STATUS

approved

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Last modified March 6 20:37 EST 2021. Contains 341850 sequences. (Running on oeis4.)