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A370192
a(n) is the numerator of the imaginary part of 1/(1+i/2)^n, where i is the imaginary unit.
2
0, -2, -16, -88, -384, -1312, -2816, 3712, 86016, 613888, 3190784, 13248512, 42172416, 72409088, -264175616, -3561586688, -23209181184, -114441715712, -451350102016, -1321966501888, -1548729974784, 14049490239488, 143370521411584, 865974366502912, 4060384503791616, 15163588700274688
OFFSET
0,2
COMMENTS
The corresponding denominators are 5^n.
FORMULA
From Stefano Spezia, Feb 17 2024: (Start)
G.f.: -2*x/(1 - 8*x + 20*x^2).
E.g.f.: -exp(4*x)*sin(2*x). (End)
EXAMPLE
n (5/(1 + i/2))^n
A370191(n) a(n)
0 1 +0 *i
1 4 -2 *i
2 12 -16 *i
3 16 -88 *i
4 -112 -384 *i
5 -1216 -1312 *i
6 -7488 -2816 *i
7 -35584 +3712 *i
8 -134912 +86016 *i
MATHEMATICA
LinearRecurrence[{8, -20}, {0, -2}, 26]
PROG
(PARI) a370192(n) = numerator(imag(1/(1+I/2)^n))
CROSSREFS
Cf. A000351 (denominators), A370191.
Sequence in context: A207655 A071893 A220505 * A069440 A000431 A281982
KEYWORD
sign,frac,easy
AUTHOR
Hugo Pfoertner, Feb 17 2024
STATUS
approved