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A047297
Numbers that are congruent to {0, 3, 4, 6} mod 7.
1
0, 3, 4, 6, 7, 10, 11, 13, 14, 17, 18, 20, 21, 24, 25, 27, 28, 31, 32, 34, 35, 38, 39, 41, 42, 45, 46, 48, 49, 52, 53, 55, 56, 59, 60, 62, 63, 66, 67, 69, 70, 73, 74, 76, 77, 80, 81, 83, 84, 87, 88, 90, 91, 94, 95, 97, 98, 101, 102, 104, 105, 108, 109, 111
OFFSET
1,2
FORMULA
G.f.: x^2*(3+x+2*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011
From Wesley Ivan Hurt, Jun 02 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14*n-9+3*i^(2*n)-(1+i)*i^(-n)-(1-i)*i^n)/8 where i=sqrt(-1).
a(2k) = A047280(k), a(2k-1) = A047345(k). (End)
MAPLE
A047297:=n->(14*n-9+3*I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/8: seq(A047297(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016
MATHEMATICA
Table[(14n-9+3*I^(2n)-(1+I)*I^(-n)-(1-I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 02 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 7 in [0, 3, 4, 6]]; // Wesley Ivan Hurt, Jun 02 2016
CROSSREFS
Sequence in context: A347752 A060832 A341292 * A183233 A191926 A065135
KEYWORD
nonn,easy
STATUS
approved