A047511 Numbers that are congruent to {0, 2, 4, 6, 7} mod 8.
0, 2, 4, 6, 7, 8, 10, 12, 14, 15, 16, 18, 20, 22, 23, 24, 26, 28, 30, 31, 32, 34, 36, 38, 39, 40, 42, 44, 46, 47, 48, 50, 52, 54, 55, 56, 58, 60, 62, 63, 64, 66, 68, 70, 71, 72, 74, 76, 78, 79, 80, 82, 84, 86, 87, 88, 90, 92, 94, 95, 96, 98, 100, 102, 103
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
Programs
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Magma
[n : n in [0..150] | n mod 8 in [0, 2, 4, 6, 7]]; // Wesley Ivan Hurt, Jul 31 2016
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Maple
A047511:=n->8*floor(n/5)+[(0, 2, 4, 6, 7)][(n mod 5)+1]: seq(A047511(n), n=0..100); # Wesley Ivan Hurt, Jul 31 2016
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Mathematica
Select[Range[0,100], MemberQ[{0,2,4,6,7}, Mod[#,8]]&] (* or *) LinearRecurrence[ {1,0,0,0,1,-1}, {0,2,4,6,7,8}, 100] (* Harvey P. Dale, May 09 2014 *)
Formula
a(0)=0, a(1)=2, a(2)=4, a(3)=6, a(4)=7, a(5)=8, a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6. - Harvey P. Dale, May 09 2014
From Wesley Ivan Hurt, Jul 31 2016: (Start)
G.f.: x^2*(2+2*x+2*x^2+x^3+x^4)/((x-1)^2*(1+x+x^2+x^3+x^4)).
a(n) = a(n-5) + 8 for n > 5.
a(n) = (40*n - 25 + 3*(n mod 5) - 2*((n+1) mod 5) - 2*((n+2) mod 5) - 2*((n+3) mod 5) + 3*((n+4) mod 5))/25.
a(5k) = 8k-1, a(5k-1) = 8k-2, a(5k-2) = 8k-4, a(5k-3) = 8k-6, a(5k-4) = 8k-8. (End)