A019493 a(n) = 3*a(n-1) - 4*a(n-3) + a(n-6).

4, 9, 20, 44, 96, 209, 455, 990, 2154, 4686, 10194, 22175, 48236, 104922, 228220, 496402, 1079712, 2348431, 5107921, 11109837, 24164007, 52556739, 114310581, 248624146, 540753403, 1176127722, 2558050589, 5563694894

Offset

0,1

References

R. K. Guy, personal communication.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,-4,0,0,1).

Formula

G.f.: (4 - 3*x - 7*x^2 + x^5)/(1 - 3*x + 4*x^3 - x^6). - R. J. Mathar, Feb 11 2016

Mathematica

LinearRecurrence[{3, 0, -4, 0, 0, 1}, {4, 9, 20, 44, 96, 209}, 30] (* G. C. Greubel, Mar 24 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((4-3*x-7*x^2+x^5 )/(1-3*x+4*x^3-x^6)) \\ G. C. Greubel, Mar 24 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (4-3*x-7*x^2+x^5 )/(1-3*x+4*x^3-x^6) )); // G. C. Greubel, Mar 24 2019
(Sage) ((4-3*x-7*x^2+x^5 )/(1-3*x+4*x^3-x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Mar 24 2019

Crossrefs

Matches A019492 up to n <= 10.

Sequence in context: A276778 A133095 A132175 * A019492 A020708 A345192

Adjacent sequences: A019490 A019491 A019492 * A019494 A019495 A019496

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved