A083031 Numbers that are congruent to {0, 3, 7} mod 12.
0, 3, 7, 12, 15, 19, 24, 27, 31, 36, 39, 43, 48, 51, 55, 60, 63, 67, 72, 75, 79, 84, 87, 91, 96, 99, 103, 108, 111, 115, 120, 123, 127, 132, 135, 139, 144, 147, 151, 156, 159, 163, 168, 171, 175, 180, 183, 187, 192, 195, 199, 204, 207, 211, 216, 219
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
Crossrefs
A guide for some sequences related to modes and chords:
Modes:
Lydian mode (F): A083089
Ionian mode (C): A083026
Mixolydian mode (G): A083120
Dorian mode (D): A083033
Phrygian mode (E): A083034
Locrian mode (B): A082977
Chords:
Major chord: A083030
Minor chord: this sequence
Dominant seventh chord: A083032
Programs
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Magma
[n : n in [0..300] | n mod 12 in [0, 3, 7]]; // Wesley Ivan Hurt, Jun 14 2016
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Maple
A083031:=n->(12*n-14-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3: seq(A083031(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016
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Mathematica
Select[Range[0, 400], MemberQ[{0, 3, 7}, Mod[#, 12]] &] (* Wesley Ivan Hurt, Jun 14 2016 *) LinearRecurrence[{1, 0, 1, -1}, {0, 3, 7, 12}, 100] (* Jianing Song, Sep 22 2018 *) -
PARI
x='x+O('x^99); concat(0, Vec(x^2*(3+4*x+5*x^2)/((1+x+x^2)*(1-x)^2))) \\ Jianing Song, Sep 22 2018
Formula
G.f.: x^2*(3 + 4*x + 5*x^2)/((1 + x + x^2)*(1 - x)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.
a(n) = (12*n - 14 - cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3))/3.
a(3k) = 12k - 5, a(3k-1) = 12k - 9, a(3k-2) = 12k - 12. (End)
a(n) = a(n-3) + 12 for n > 3. - Jianing Song, Sep 22 2018
Comments