A175715 Expansion of 1/(1 - x - x^2 - 3*x^4 + 4*x^5 - 2*x^6).

1, 1, 2, 3, 8, 10, 22, 35, 73, 112, 227, 376, 726, 1216, 2321, 3981, 7430, 12907, 23888, 41886, 76782, 135631, 247309, 438860, 796747, 1419144, 2568858, 4586608, 8284885, 14819657, 26728034, 47870371, 86244344, 154607362, 278326950, 499272603, 898307169

Offset

0,3

Comments

The ratio a(n+1)/a(n) approaches 1.796757012458598901977511048324681177...

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,1,0,3,-4,2).

Formula

G.f.: 1/(1 - x - x^2 - 3*x^4 + 4*x^5 - 2*x^6).

Maple

seq(coeff(series(1/(1-x-x^2-3*x^4+4*x^5-2*x^6), x, n+1), x, n), n = 0..40); # G. C. Greubel, Dec 04 2019

Mathematica

LinearRecurrence[{1, 1, 0, 3, -4, 2}, {1, 1, 2, 3, 8, 10}, 40] (* Bruno Berselli, May 17 2017 *)

Prog

(PARI) my(x='x+O('x^40)); Vec(1/(1-x-x^2-3*x^4+4*x^5-2*x^6)) \\ G. C. Greubel, Dec 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-x-x^2-3*x^4+4*x^5-2*x^6) )); // G. C. Greubel, Dec 04 2019
(Sage)
def A175715_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x-x^2-3*x^4+4*x^5-2*x^6) ).list()
A175715_list(40) # G. C. Greubel, Dec 04 2019
(GAP) a:=[1, 1, 2, 3, 8, 10];; for n in [7..30] do a[n]:=a[n-1]+a[n-2]+3*a[n-4] - 4*a[n-5]+2*a[n-6]; od; a; # G. C. Greubel, Dec 04 2019

Crossrefs

Sequence in context: A083799 A098844 A034437 * A329582 A138880 A063474

Adjacent sequences: A175712 A175713 A175714 * A175716 A175717 A175718

Keyword

nonn,easy

Author

Roger L. Bagula, Dec 04 2010

Status

approved