A135263 a(n) = 2*A132357(n).

2, 8, 28, 82, 244, 728, 2186, 6560, 19684, 59050, 177148, 531440, 1594322, 4782968, 14348908, 43046722, 129140164, 387420488, 1162261466, 3486784400, 10460353204, 31381059610, 94143178828, 282429536480, 847288609442

Offset

0,1

Comments

Digital roots yield a hexaperiodic sequence A010888(a(n))= 2, (8, 1, 1, 1, 8, 8,...), the period of length 6 put in parenthesis. Digital roots of A132357 are also hexaperiodic: 1, (4, 5, 5, 5, 4, 4, ....).

Links

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

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

Formula

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

G.f.: 2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2)). - Colin Barker, Jun 16 2012

Maple

seq(coeff(series(2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2)), x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 21 2019

Mathematica

LinearRecurrence[{3, 0, -1, 3}, {2, 8, 28, 82}, 30] (* G. C. Greubel, Oct 07 2016 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2))) \\ G. C. Greubel, Nov 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2)) )); // G. C. Greubel, Nov 21 2019
(Sage)
def A135263_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2))).list()
A135263_list(30) # G. C. Greubel, Nov 21 2019
(GAP) a:=[2, 8, 28, 82];; for n in [5..30] do a[n]:=3*a[n-1]-a[n-3]+ 3*a[n-4]; od; a; # G. C. Greubel, Nov 21 2019

Crossrefs

Cf. A133448 (hexaperiodic sequence of digital roots).

Sequence in context: A245996 A229935 A082107 * A048497 A118047 A087431

Adjacent sequences: A135260 A135261 A135262 * A135264 A135265 A135266

Keyword

nonn,less,easy

Author

Paul Curtz, Dec 02 2007

Extensions

Edited and extended by R. J. Mathar, Jul 22 2008

Status

approved