A037578 Base 6 digits are, in order, the first n terms of the periodic sequence with initial period 1,3.

1, 9, 55, 333, 1999, 11997, 71983, 431901, 2591407, 15548445, 93290671, 559744029, 3358464175, 20150785053, 120904710319, 725428261917, 4352569571503, 26115417429021, 156692504574127, 940155027444765, 5640930164668591, 33845580988011549, 203073485928069295

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,1,-6).

Formula

a(n) = 5*a(n-1) + 6*a(n-2) + 4, a(0)=0, a(1)=1. - Zerinvary Lajos, Dec 14 2008

From R. J. Mathar, Oct 05 2009: (Start)

a(n) = 6*a(n-1) + a(n-2) - 6*a(n-3).

a(n) = 9*6^n/35 - 2/5 + (-1)^n/7. (End)

G.f.: x*(3*x+1)/((x-1)*(x+1)*(6*x-1)). - Colin Barker, Dec 27 2012

E.g.f.: exp(-x)*(5 - 14*exp(2*x) + 9*exp(7*x))/35. - Elmo R. Oliveira, Dec 27 2025

Maple

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=5*a[n-1]+6*a[n-2]+4 od: seq(a[n], n=1..33); # Zerinvary Lajos, Dec 14 2008

Mathematica

CoefficientList[Series[(3 x + 1)/((x - 1) (x + 1) (6 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Prog

(Magma) [9*6^n/35-2/5+(-1)^n/7: n in [1..30]]; // Vincenzo Librandi, Oct 21 2013

Crossrefs

Cf. A007092.

Cf. A037576, A037577, A037579, A037580, A037581, A037582.

Sequence in context: A356339 A362365 A183805 * A389322 A096191 A362088

Adjacent sequences: A037575 A037576 A037577 * A037579 A037580 A037581

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved