|
|
A047286
|
|
Numbers that are congruent to {1, 2, 3, 6} mod 7.
|
|
1
|
|
|
1, 2, 3, 6, 8, 9, 10, 13, 15, 16, 17, 20, 22, 23, 24, 27, 29, 30, 31, 34, 36, 37, 38, 41, 43, 44, 45, 48, 50, 51, 52, 55, 57, 58, 59, 62, 64, 65, 66, 69, 71, 72, 73, 76, 78, 79, 80, 83, 85, 86, 87, 90, 92, 93, 94, 97, 99, 100, 101, 104, 106, 107, 108, 111
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(1+x+x^2+3*x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14n-11+i^(2n)+(1+3i)*i^(-n)+(1-3i)*i^n)/8 where i=sqrt(-1).
E.g.f.: (4 + 3*sin(x) + cos(x) + (7*x - 6)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, May 23 2016
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[(14n-11+I^(2n)+(1+3I)*I^(-n)+(1-3I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 22 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 3, 6, 8}, 80] (* Vincenzo Librandi, May 24 2016 *)
|
|
PROG
|
(Magma) [n : n in [0..150] | n mod 7 in [1, 2, 3, 6]]; // Wesley Ivan Hurt, May 22 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|