A047574 Numbers that are congruent to {5, 6, 7} mod 8.
5, 6, 7, 13, 14, 15, 21, 22, 23, 29, 30, 31, 37, 38, 39, 45, 46, 47, 53, 54, 55, 61, 62, 63, 69, 70, 71, 77, 78, 79, 85, 86, 87, 93, 94, 95, 101, 102, 103, 109, 110, 111, 117, 118, 119, 125, 126, 127, 133, 134, 135, 141, 142, 143, 149, 150, 151, 157, 158, 159
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
Programs
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Magma
[n: n in [0..200] | n mod 8 in [5..7]]; // Vincenzo Librandi, May 30 2016
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Maple
A047574:=n->8*floor((n-1)/3)+((n-1) mod 3)+5: seq(A047574(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016
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Mathematica
Select[Range[200], MemberQ[{5, 6, 7}, Mod[#, 8]] &] (* Vincenzo Librandi, May 30 2016 *) LinearRecurrence[{1,0,1,-1},{5,6,7,13},60] (* Harvey P. Dale, Jul 29 2016 *) -
PARI
a(n)=8 * (n-1)\3 + (n-1)%3 + 5 \\ David A. Corneth, May 30 2016
Formula
From Chai Wah Wu, May 30 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
G.f.: x*(x^3 + x^2 + x + 5)/(x^4 - x^3 - x + 1). (End)
a(n) = (8*n-10*sin(2*Pi*(n+1)/3)/sqrt(3)+2)/3. - Ilya Gutkovskiy, May 30 2016
a(n) = 8*floor((n-1)/3)+((n-1) mod 3)+5. - David A. Corneth, May 30 2016
a(3k) = 8k-1, a(3k-1) = 8k-2, a(3k-2) = 8k-3. - Wesley Ivan Hurt, Jun 10 2016