A342154 - OEIS

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A342154

Number of partitions of n^5 into two positive squares.

1

0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 3, 0, 0, 3, 0, 0, 0, 3, 1, 0, 3, 0, 0, 0, 0, 5, 3, 0, 0, 3, 0, 0, 1, 0, 3, 0, 0, 3, 0, 0, 3, 3, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 18, 0, 0, 3, 0, 0, 0, 1, 3, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 18, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 1, 0, 5, 3, 0, 0, 3, 0

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OFFSET

0,6

COMMENTS

a(n) > 0 if and only if n is in A000404. - Robert Israel, Mar 03 2021

LINKS

Robert Israel, Table of n, a(n) for n = 0..3050

Index entries for sequences related to sums of squares

FORMULA

a(n) = A025426(A000584(n)).

EXAMPLE

2^5 = 32 = 4^2 + 4^2. So a(2) = 1.

5^5 = 3125 = 10^2 + 55^2 = 25^2 + 50^2 = 38^2 + 41^2. So a(5) = 3.

MAPLE

f:= proc(n) local x, y, S;

S:= map(t -> subs(t, [x, y]), [isolve(x^2+y^2=n^5)]);

nops(select(t -> t[1] >= t[2] and t[2] > 0, S))

end proc:

map(f, [$0..200]); # Robert Israel, Mar 03 2021

PROG

(PARI) a(n) = my(cnt=0, m=n^5); for(k=1, sqrt(m/2), l=m-k*k; if(l>0&&issquare(l), cnt++)); cnt;

CROSSREFS

Cf. A000404, A000584, A025426, A046080, A084888.

Sequence in context: A324864 A331509 A171913 * A074936 A035655 A353323

Adjacent sequences: A342151 A342152 A342153 * A342155 A342156 A342157

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Mar 02 2021

STATUS

approved