A370192 a(n) is the numerator of the imaginary part of 1/(1+i/2)^n, where i is the imaginary unit.

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.

Links

Hugo Pfoertner, Table of n, a(n) for n = 0..300

Hugo Pfoertner Plot of asinh(A370192(n)) vs asinh(A370191(n)), using Plot 2.

Index entries for linear recurrences with constant coefficients, signature (8,-20).

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

Adjacent sequences: A370189 A370190 A370191 * A370193 A370194 A370195

Keyword

sign,frac,easy

Author

Hugo Pfoertner, Feb 17 2024

Status

approved