A153267 a(n) = -4*a(n-3) + 11*a(n-2) - a(n-1), a(0) = -5, a(1) = 39, a(2) = -110.

-5, 39, -110, 559, -1925, 8514, -31925, 133279, -518510, 2112279, -8349005, 33658114, -133946285, 537581559, -2145623150, 8594805439, -34346986325, 137472338754, -549668410085, 2199252081679, -8795493947630, 35185940486439

Offset

0,1

Comments

A153266(n) + a(n) = 4*A001519(n) (apart from initial terms). The generating floretion Z = X*Y with X = 1.5'i + 0.5i' + .25(ii + jj + kk + ee) and Y = 0.5'i + 1.5i' + .25(ii + jj + kk + ee).

Links

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

Index entries for linear recurrences with constant coefficients, signature (-1, 11, -4).

Formula

a(n) = 2*(-4)^n + 3/2+1/2*sqrt(5))^n + (3/2-1/2*sqrt(5))^n.

G.f.: -(16*x^2-34*x+5) / ((4*x+1)*(x^2-3*x+1)). - Colin Barker, Jun 25 2014

Example

a(4) = -1*559 + 11*(-110) - 4*(39) = -1925.

Mathematica

CoefficientList[Series[-(16 x^2 - 34 x + 5)/((4 x + 1) (x^2 - 3 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 26 2014 *)
LinearRecurrence[{-1, 11, -4}, {-5, 39, -110}, 30] (* Harvey P. Dale, Mar 02 2023 *)

Prog

(PARI) Vec(-(16*x^2-34*x+5)/((4*x+1)*(x^2-3*x+1)) + O(x^100)) \\ Colin Barker, Jun 25 2014

Crossrefs

Cf. A153266, A153265, A001519.

Sequence in context: A095230 A247708 A171555 * A183477 A219086 A064445

Adjacent sequences: A153264 A153265 A153266 * A153268 A153269 A153270

Keyword

easy,sign

Author

Creighton Dement, Jan 02 2009

Status

approved