A047434 Numbers that are congruent to {0, 2, 4, 5, 6} mod 8.
0, 2, 4, 5, 6, 8, 10, 12, 13, 14, 16, 18, 20, 21, 22, 24, 26, 28, 29, 30, 32, 34, 36, 37, 38, 40, 42, 44, 45, 46, 48, 50, 52, 53, 54, 56, 58, 60, 61, 62, 64, 66, 68, 69, 70, 72, 74, 76, 77, 78, 80, 82, 84, 85, 86, 88, 90, 92, 93, 94, 96, 98, 100, 101, 102
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
Programs
-
Magma
[n : n in [0..150] | n mod 8 in [0, 2, 4, 5, 6]]; // Wesley Ivan Hurt, Aug 01 2016
-
Maple
A047434:=n->8*floor(n/5)+[(0, 2, 4, 5, 6)][(n mod 5)+1]: seq(A047434(n), n=0..100); # Wesley Ivan Hurt, Aug 01 2016
-
Mathematica
Select[Range[0, 100], MemberQ[{0, 2, 4, 5, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Aug 01 2016 *)
Formula
G.f.: x^2*(2+2*x+x^2+x^3+2*x^4) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011
From Wesley Ivan Hurt, Aug 01 2016: (Start)
a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.
a(n) = (40*n - 35 + 3*(n mod 5) + 3*((n+1) mod 5) - 2*((n+2) mod 5) - 2*((n+3) mod 5) - 2*((n+4) mod 5))/25.
a(5k) = 8k-2, a(5k-1) = 8k-3, a(5k-2) = 8k-4, a(5k-3) = 8k-6, a(5k-4) = 8k-8. (End)