A047379 Numbers that are congruent to {0, 2, 4, 5} mod 7.
0, 2, 4, 5, 7, 9, 11, 12, 14, 16, 18, 19, 21, 23, 25, 26, 28, 30, 32, 33, 35, 37, 39, 40, 42, 44, 46, 47, 49, 51, 53, 54, 56, 58, 60, 61, 63, 65, 67, 68, 70, 72, 74, 75, 77, 79, 81, 82, 84, 86, 88, 89, 91, 93, 95, 96
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
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Magma
[Floor((7*n-5)/4) : n in [1..100]]; // Wesley Ivan Hurt, Dec 03 2014
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Maple
A047379:=n->floor((7*n-5)/4): seq(A047379(n), n=1..100); # Wesley Ivan Hurt, Dec 03 2014
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Mathematica
Select[Range[0,100],MemberQ[{0,2,4,5},Mod[#,7]]&] (* Harvey P. Dale, Apr 10 2014 *)
Formula
a(n) = floor(floor((7n + 2)/2)/2).
a(n) = floor((7n-5)/4). - Gary Detlefs, Mar 07 2010
G.f.: x^2*(2+2*x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011
From Wesley Ivan Hurt, Dec 03 2014: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5), n>5;
a(n) = (14*n-13-(-1)^n+2*i^n*(-1)^((3+(-1)^n)/4))/8, where i = sqrt(-1);