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A364033
Expansion of Sum_{k>0} k * x^(3*k) / (1 + x^(4*k)).
1
0, 0, 1, 0, 0, 2, -1, 0, 3, 0, 1, 4, 0, -2, 4, 0, 0, 6, 1, 0, 4, 2, -1, 8, 0, 0, 10, -4, 0, 8, -1, 0, 14, 0, -4, 12, 0, 2, 12, 0, 0, 8, 1, 4, 12, -2, -1, 16, -7, 0, 18, 0, 0, 20, 4, -8, 22, 0, 1, 16, 0, -2, 11, 0, 0, 28, 1, 0, 20, -8, -1, 24, 0, 0, 21, 4, -4, 24, -1, 0, 30, 0, 1, 16, 0, 2, 28, 8, 0, 24, -12
OFFSET
1,6
FORMULA
G.f.: Sum_{k>0} (-1)^(k-1) * x^(4*k-1) / (1 - x^(4*k-1))^2.
a(n) = Sum_{d|n, d==3 (mod 4)} (-1)^((d-3)/4) * (n/d).
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^((#-3)/4) * (n/#) &, Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Jul 02 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d%4==3)*(-1)^((d-3)/4)*n/d);
CROSSREFS
Cf. A364032.
Sequence in context: A284950 A308298 A364106 * A050464 A014405 A368464
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 01 2023
STATUS
approved