A083030 Numbers that are congruent to {0, 4, 7} mod 12.
0, 4, 7, 12, 16, 19, 24, 28, 31, 36, 40, 43, 48, 52, 55, 60, 64, 67, 72, 76, 79, 84, 88, 91, 96, 100, 103, 108, 112, 115, 120, 124, 127, 132, 136, 139, 144, 148, 151, 156, 160, 163, 168, 172, 175, 180, 184, 187, 192, 196, 199, 204, 208, 211, 216, 220
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: this sequence
Minor chord: A083031
Dominant seventh chord: A083032
Programs
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Magma
[n : n in [0..300] | n mod 12 in [0, 4, 7]]; // Wesley Ivan Hurt, Jun 14 2016
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Maple
A083030:=n->4*n-(13+2*cos(2*n*Pi/3))/3: seq(A083030(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016
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Mathematica
Select[Range[0,250], MemberQ[{0,4,7}, Mod[#,12]]&] (* Harvey P. Dale, Apr 17 2014 *) LinearRecurrence[{1, 0, 1, -1}, {0, 4, 7, 12}, 100] (* Jianing Song, Sep 22 2018 *) -
PARI
my(x='x+O('x^99)); concat(0, Vec(x^2*(4+3*x+5*x^2)/((1+x+x^2)*(1-x)^2))) \\ Jianing Song, Sep 22 2018
Formula
G.f.: x^2*(4 + 3*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) = 4*n - (13 + 2*cos(2*n*Pi/3))/3.
a(3k) = 12k - 5, a(3k-1) = 12k - 8, a(3k-2) = 12k - 12. (End)
a(n) = a(n-3) + 12 for n > 3. - Jianing Song, Sep 22 2018
Comments