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

Author

Paul Curtz, Dec 02 2007

Keywords

• nonn
• less
• easy

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).

Crossrefs

Cf. A133448 (hexaperiodic sequence of digital roots).

Programs

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

Magma

R:=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

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 *)

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

Sage

def A135263_list(prec):
    P. = 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

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

Extensions

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