A369732 -id:A369732 - cp's OEIS frontend

A369730 Number of solutions to +- 1^2 +- 2^2 +- 3^2 +- ... +- n^2 = 1.

0, 1, 0, 0, 0, 0, 2, 0, 0, 5, 2, 0, 0, 13, 43, 0, 0, 193, 274, 0, 0, 1552, 3245, 0, 0, 18628, 31048, 0, 0, 188536, 372710, 0, 0, 2376996, 4197425, 0, 0, 27465147, 53072709, 0, 0, 351329160, 650125358, 0, 0, 4398613111, 8429649875, 0, 0, 57629346805, 108986428106

Offset: 0

Ilya Gutkovskiy, Jan 30 2024

nonn

Cf. A000290, A063866, A158092, A348165, A350403, A369731, A369732.

b:= proc(n, i) option remember; `if`(n>i*(i+1)*(2*i+1)/6, 0,
      `if`(i=0, 1, b(n+i^2, i-1)+b(abs(n-i^2), i-1)))
    end:
a:=n-> b(1, n):
seq(a(n), n=0..50);  # Alois P. Heinz, Jan 30 2024

Table[Coefficient[Product[(x^(k^2) + 1/x^(k^2)), {k, 1, n}], x, 1], {n, 0, 48}]

a(n) = [x^1] Product_{k=1..n} (x^(k^2) + 1/x^(k^2)).

A369731 Number of solutions to +- 1^3 +- 2^3 +- 3^3 +- ... +- n^3 = 1.

Original entry on oeis.org

0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 1, 0, 0, 6, 1, 0, 0, 12, 344, 0, 0, 1140, 713, 0, 0, 4384, 5956, 0, 0, 48774, 197767, 0, 0, 1147500, 1097442, 0, 0, 6499466, 11844316, 0, 0, 85185855, 261696060, 0, 0, 1649383741, 2039067290, 0, 0, 13301106607, 25603704324

Offset: 0

Ilya Gutkovskiy, Jan 30 2024

nonn

Cf. A000578, A063866, A158118, A348892, A350861, A369730, A369732.

Table[Coefficient[Product[(x^(k^3) + 1/x^(k^3)), {k, 1, n}], x, 1], {n, 0, 50}]

a(n) = [x^1] Product_{k=1..n} (x^(k^3) + 1/x^(k^3)).

cp's OEIS Frontend

A369730 Number of solutions to +- 1^2 +- 2^2 +- 3^2 +- ... +- n^2 = 1.

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