|
|
A047392
|
|
Numbers that are congruent to {0, 1, 3, 5} mod 7.
|
|
3
|
|
|
0, 1, 3, 5, 7, 8, 10, 12, 14, 15, 17, 19, 21, 22, 24, 26, 28, 29, 31, 33, 35, 36, 38, 40, 42, 43, 45, 47, 49, 50, 52, 54, 56, 57, 59, 61, 63, 64, 66, 68, 70, 71, 73, 75, 77, 78, 80, 82, 84, 85, 87, 89, 91, 92, 94, 96, 98, 99, 101, 103, 105, 106, 108, 110
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x^2*(1+2*x+2*x^2+2*x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14*n - 17 - i^(2*n) + (1 + i)*i^(-n) + (1 - i)*i^n)/8.
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[(14n-17-I^(2n)+(1+I)*I^(-n)+(1-I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 21 2016 *)
Table[n + Floor[3 n/4 - 3/4] - 1, {n, 1, 70}] (* Bruno Berselli, Jun 15 2016 *)
|
|
PROG
|
(Magma) [n: n in [0..100] | n mod 7 in [0, 1, 3, 5]]; // Wesley Ivan Hurt, May 21 2016
|
|
CROSSREFS
|
Cf. A047371: n + floor(3*n/4-1/2) - 1; A047379: n + floor(3*n/4-1/4) - 1.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|