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A047354
Numbers that are congruent to {0, 1, 2} mod 7.
2
0, 1, 2, 7, 8, 9, 14, 15, 16, 21, 22, 23, 28, 29, 30, 35, 36, 37, 42, 43, 44, 49, 50, 51, 56, 57, 58, 63, 64, 65, 70, 71, 72, 77, 78, 79, 84, 85, 86, 91, 92, 93, 98, 99, 100, 105, 106, 107, 112, 113, 114, 119, 120, 121, 126, 127, 128, 133, 134, 135, 140, 141
OFFSET
1,3
FORMULA
a(n) = 7*floor(n/3)+(n mod 3), with offset 0 and a(0)=0. - Gary Detlefs, Mar 09 2010
From R. J. Mathar, Mar 29 2010: (Start)
G.f.: x^2*(1+x+5*x^2)/((1+x+x^2) * (x-1)^2).
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. (End)
a(n+1) = Sum_{k>=0} A030341(n,k)*b(k) with b(0)=1 and b(k)=7*3^(k-1) for k>0. - Philippe Deléham, Oct 24 2011
From Wesley Ivan Hurt, Jun 08 2016: (Start)
a(n) = (21*n-33-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 7k-5, a(3k-1) = 7k-6, a(3k-2) = 7k-7. (End)
a(n) = n + 4*floor((n-1)/3) - 1. - Bruno Berselli, Feb 06 2017
MAPLE
seq(7*floor(n/3)+(n mod 3), n=0..60); # Gary Detlefs, Mar 09 2010
MATHEMATICA
Flatten[{#, #+1, #+2}&/@(7Range[0, 20])] (* Harvey P. Dale, Mar 05 2011 *)
PROG
(Magma) [n : n in [0..150] | n mod 7 in [0..2]]; // Wesley Ivan Hurt, Jun 08 2016
CROSSREFS
Cf. A030341.
Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.
Sequence in context: A287515 A260581 A179772 * A037455 A020675 A317303
KEYWORD
nonn,easy
STATUS
approved