|
|
A047366
|
|
Numbers that are congruent to {1, 3, 4, 5} mod 7.
|
|
1
|
|
|
1, 3, 4, 5, 8, 10, 11, 12, 15, 17, 18, 19, 22, 24, 25, 26, 29, 31, 32, 33, 36, 38, 39, 40, 43, 45, 46, 47, 50, 52, 53, 54, 57, 59, 60, 61, 64, 66, 67, 68, 71, 73, 74, 75, 78, 80, 81, 82, 85, 87, 88, 89, 92, 94, 95, 96, 99, 101, 102, 103, 106, 108, 109, 110
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(1+2*x+x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14n-9-i^(2n)-(3-i)*i^(-n)-(3+i)*i^n)/8 where i=sqrt(-1).
E.g.f.: (8 + sin(x) - 3*cos(x) + (7*x - 4)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, May 25 2016
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[(14n-9-I^(2n)-(3-I)*I^(-n)-(3+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *)
Select[Range@ 120, MemberQ[{1, 3, 4, 5}, Mod[#, 7]] &] (* Michael De Vlieger, May 24 2016 *)
|
|
PROG
|
(Magma) [n : n in [0..150] | n mod 7 in [1, 3, 4, 5]]; // Wesley Ivan Hurt, May 24 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|