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A014291 Imaginary Rabbits: imaginary part of a(0)=i; a(1)=-i; a(n) = a(n-1) + i*a(n-2), with i = sqrt(-1). 2
1, -1, -1, -1, -2, -2, -1, 1, 5, 11, 18, 24, 25, 15, -13, -65, -142, -234, -313, -327, -199, 163, 838, 1840, 3041, 4079, 4279, 2639, -2042, -10802, -23841, -39519, -53155, -55989, -34982, 25544, 139225, 308895, 513547, 692655 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Second differences give -a(n-2).

REFERENCES

Charles Gely, "Lapins imaginaires et valeurs propres". Quadrature Quarterly #30.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,-1).

FORMULA

a(n) = 2*a(n-1) - a(n-2) - a(n-4).

G.f.: (1-x)*(1-2*x)/(1-2*x+x^2+x^4).

a(n) = Im( -i*J(n, -i) + J(n-1, -i) ), where J(n,x) is the Jacobsthal polynomial, whose coefficient array is A128099, and i = sqrt(-1). - G. C. Greubel, Jun 15 2019

MATHEMATICA

CoefficientList[Series[(2*x-1)*(x-1)/(x^4+x^2-2*x+1), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 23 2012 *)

PROG

(MAGMA) I:=[1, -1, -1, -1]; [n le 4 select I[n] else 2*Self(n-1) - Self(n-2) - Self(n-4): n in [1..50]]; // Vincenzo Librandi, Oct 23 2012

(PARI) my(x='x+O('x^50)); Vec((1-x)*(1-2*x)/(1-2*x+x^2+x^4)) \\ G. C. Greubel, Jun 13 2019

(Sage) ((1-x)*(1-2*x)/(1-2*x+x^2+x^4)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 13 2019

(GAP) a:=[1, -1, -1, -1];; for n in [5..50] do a[n]:=2*a[n-1]-a[n-2]-a[n-4]; od; a; # G. C. Greubel, Jun 13 2019

CROSSREFS

Cf. A128099.

Sequence in context: A177694 A092450 A279629 * A136587 A136247 A086610

Adjacent sequences:  A014288 A014289 A014290 * A014292 A014293 A014294

KEYWORD

sign,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified July 17 14:44 EDT 2019. Contains 325106 sequences. (Running on oeis4.)