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

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]

a(n)= 6*a(n-1) +a(n-2) -6*a(n-3). a(n) = 9*6^n/35 - 2/5 + (-1)^n/7. [R. J. Mathar, Oct 05 2009]

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

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

Sequence in context: A356339 A362365 A183805 * A096191 A362088 A281454

Adjacent sequences: A037575 A037576 A037577 * A037579 A037580 A037581

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved