|
|
A037691
|
|
Base-7 digits are, in order, the first n terms of the periodic sequence with initial period 1,2,0,3.
|
|
2
|
|
|
1, 9, 63, 444, 3109, 21765, 152355, 1066488, 7465417, 52257921, 365805447, 2560638132, 17924466925, 125471268477, 878298879339, 6148092155376, 43036645087633, 301256515613433, 2108795609294031, 14761569265058220, 103330984855407541, 723316893987852789
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 7*a(n-1) + a(n-4) - 7*a(n-5).
a(n) = 1/200*(25*(-1)^n-(6-8*i)*(-i)^n-(6+8*i)*i^n+37*7^n-50) where i=sqrt(-1).
G.f.: x*(1+2*x+3*x^3) / ((1-x)*(1+x)*(1-7*x)*(1+x^2)).
(End)
|
|
MATHEMATICA
|
Table[FromDigits[PadRight[{}, n, {1, 2, 0, 3}], 7], {n, 30}] (* Harvey P. Dale, May 24 2017 *)
|
|
PROG
|
(PARI) Vec(x*(1+2*x+3*x^3)/((1-x)*(1+x)*(1-7*x)*(1+x^2)) + O(x^30)) \\ Colin Barker, Dec 24 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|