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A135264 a(n) = 3*A132357(n). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

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]

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 *)

PROG

(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

(MAGMA) R<x>:=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

(Sage)

def A135264_list(prec):

    P.<x> = 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

(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

CROSSREFS

Sequence in context: A038342 A260153 A328299 * A084529 A017941 A066972

Adjacent sequences:  A135261 A135262 A135263 * A135265 A135266 A135267

KEYWORD

nonn,less,easy

AUTHOR

Paul Curtz, Dec 02 2007

EXTENSIONS

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

STATUS

approved

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Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)