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A083030
Numbers that are congruent to {0, 4, 7} mod 12.
15
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
1,2
COMMENTS
Key-numbers of the pitches of a major common chord on a standard chromatic keyboard, with root = 0.
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
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
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 *)
PROG
(Magma) [n : n in [0..300] | n mod 12 in [0, 4, 7]]; // Wesley Ivan Hurt, Jun 14 2016
(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
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
Aeolian mode (A): A060107 (raised seventh: A083028)
Phrygian mode (E): A083034
Locrian mode (B): A082977
Chords:
Major chord: this sequence
Minor chord: A083031
Dominant seventh chord: A083032
Sequence in context: A076295 A280101 A310779 * A310780 A285961 A310781
KEYWORD
nonn,easy
AUTHOR
James Ingram (j.ingram(AT)t-online.de), Jun 01 2003
STATUS
approved