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A364032
Expansion of Sum_{k>0} x^(3*k) / (1 + x^(4*k)).
2
0, 0, 1, 0, 0, 1, -1, 0, 1, 0, 1, 1, 0, -1, 0, 0, 0, 1, 1, 0, 0, 1, -1, 1, 0, 0, 2, -1, 0, 0, -1, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, -1, -1, 1, -1, 0, 2, 0, 0, 2, 0, -1, 2, 0, 1, 0, 0, -1, -1, 0, 0, 2, 1, 0, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1, 0, 2, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, -1, 3, 0, 0
OFFSET
1,27
FORMULA
G.f.: Sum_{k>0} (-1)^(k-1) * x^(4*k-1) / (1 - x^(4*k-1)).
a(n) = Sum_{d|n, d==3 (mod 4)} (-1)^((d-3)/4).
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^((# - 3)/4) &, Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d%4==3)*(-1)^((d-3)/4));
CROSSREFS
Cf. A364033.
Sequence in context: A247763 A065360 A352512 * A333397 A101676 A056560
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 01 2023
STATUS
approved