A135264 a(n) = 3*A132357(n).

3, 12, 42, 123, 366, 1092, 3279, 9840, 29526, 88575, 265722, 797160, 2391483, 7174452, 21523362, 64570083, 193710246, 581130732, 1743392199, 5230176600, 15690529806, 47071589415, 141214768242, 423644304720, 1270932914163

Offset: 0

Author

Paul Curtz, Dec 02 2007

Keywords

• nonn
• less
• easy

Comments

Digital roots yield a hexaperiodic sequence A010888(a(n))= 3*A135265(n+1).

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).

Programs

GAP

a:=[3,12,42,123];; 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!( 3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4) )); // G. C. Greubel, Nov 21 2019

Maple

seq(coeff(series(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4), x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 21 2019

Mathematica

LinearRecurrence[{3,0,-1,3}, {3,12,42,123}, 25] (* G. C. Greubel, Oct 07 2016 *)

PARI

my(x='x+O('x^30)); Vec(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4)) \\ G. C. Greubel, Nov 21 2019

Sage

def A135264_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4)).list()
A135264_list(30) # G. C. Greubel, Nov 21 2019

Formula

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

G.f.: 3*(1 + x + 2*x^2)/(1 - 3*x + x^3 - 3*x^4). - G. C. Greubel, Oct 07 2016 [corrected by Georg Fischer, May 10 2019]

Extensions

Edited, corrected and extended by R. J. Mathar, Jul 28 2008