|
|
A047364
|
|
Numbers that are congruent to {3, 4, 5} mod 7.
|
|
1
|
|
|
3, 4, 5, 10, 11, 12, 17, 18, 19, 24, 25, 26, 31, 32, 33, 38, 39, 40, 45, 46, 47, 52, 53, 54, 59, 60, 61, 66, 67, 68, 73, 74, 75, 80, 81, 82, 87, 88, 89, 94, 95, 96, 101, 102, 103, 108, 109, 110, 115, 116, 117, 122, 123, 124, 129, 130, 131, 136, 137, 138, 143
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(3+x+x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 04 2011
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (21*n-6-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 7k-2, a(3k-1) = 7k-3, a(3k-2) = 7k-4. (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
LinearRecurrence[{1, 0, 1, -1}, {3, 4, 5, 10}, 60] (* Harvey P. Dale, Dec 03 2014 *)
Flatten[# + {3, 4, 5} & /@ (7 Range[0, 20])] (* or *)
Select[Range[0, 150], MemberQ[{3, 4, 5}, Mod[#, 7]] &] (* Robert G. Wilson v, Sep 26 2016 *)
|
|
PROG
|
(Magma) [n : n in [0..150] | n mod 7 in [3..5]]; // Wesley Ivan Hurt, Jun 08 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|