|
| |
|
|
A033116
|
|
Base-6 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.
|
|
6
|
|
|
|
1, 6, 37, 222, 1333, 7998, 47989, 287934, 1727605, 10365630, 62193781, 373162686, 2238976117, 13433856702, 80603140213, 483618841278, 2901713047669, 17410278286014, 104461669716085, 626770018296510, 3760620109779061
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
