A033116 Base-6 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.

1, 6, 37, 222, 1333, 7998, 47989, 287934, 1727605, 10365630, 62193781, 373162686, 2238976117, 13433856702, 80603140213, 483618841278, 2901713047669, 17410278286014, 104461669716085, 626770018296510, 3760620109779061

Offset

1,2

Comments

Partial sums of A015540. - Mircea Merca, Dec 28 2010

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

From R. J. Mathar, Jan 08 2011: (Start)

G.f.: x / ( (1-x)*(1-6*x)*(1+x) ).

a(n) = 6^(n+1)/35 -1/10 -(-1)^n/14. (End)

a(n)=floor(6^(n+1)/35). a(n+1)=sum{k=0..floor(n/2)} 6^(n-2*k). a(n+1)=sum{k=0..n} sum{j=0..k} (-1)^(j+k)*6^j. - Paul Barry, Nov 12 2003, index corrected R. J. Mathar, Jan 08 2011

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

a(n) = floor(6^(n+1)/7)/5 = floor((6*6^n-1)/35) = round((12*6^n-7)/70) = round((6*6^n-6)/35) = ceiling((6*6^n-6)/35). a(n)=a(n-2)+6^(n-1), n>2. - Mircea Merca, Dec 28 2010

Maple

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=5*a[n-1]+6*a[n-2]+1 od: seq(a[n], n=1..33); # Zerinvary Lajos, Dec 14 2008
A033116 := proc(n) 6^(n+1)/35 -1/10 -(-1)^n/14 ; end proc: # R. J. Mathar, Jan 08 2011

Mathematica

Join[{a=1, b=6}, Table[c=5*b+6*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2011 *)

Prog

(Magma) [Round((12*6^n-7)/70): n in [1..30]]; // Vincenzo Librandi, Jun 25 2011

Crossrefs

Cf. A015540

Sequence in context: A001419 A081152 A244618 * A033124 A288786 A180032

Adjacent sequences: A033113 A033114 A033115 * A033117 A033118 A033119

Keyword

nonn,easy,base

Author

Clark Kimberling

Status

approved