A083028 Numbers that are congruent to {0, 2, 3, 5, 7, 8, 11} mod 12.
0, 2, 3, 5, 7, 8, 11, 12, 14, 15, 17, 19, 20, 23, 24, 26, 27, 29, 31, 32, 35, 36, 38, 39, 41, 43, 44, 47, 48, 50, 51, 53, 55, 56, 59, 60, 62, 63, 65, 67, 68, 71, 72, 74, 75, 77, 79, 80, 83, 84, 86, 87, 89, 91, 92, 95, 96, 98, 99, 101, 103, 104, 107, 108, 110, 111
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-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
Aeolian mode (A): A060107 (raised seventh: this sequence)
Phrygian mode (E): A083034
Locrian mode (B): A082977
Chords:
Major chord: A083030
Minor chord: A083031
Dominant seventh chord: A083032
Programs
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Magma
[n : n in [0..150] | n mod 12 in [0, 2, 3, 5, 7, 8, 11]]; // Wesley Ivan Hurt, Jul 19 2016
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Maple
A083028:=n->12*floor(n/7)+[0, 2, 3, 5, 7, 8, 11][(n mod 7)+1]: seq(A083028(n), n=0..100); # Wesley Ivan Hurt, Jul 19 2016
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Mathematica
Select[Range[0, 150], MemberQ[{0, 2, 3, 5, 7, 8, 11}, Mod[#, 12]] &] (* Wesley Ivan Hurt, Jul 19 2016 *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 3, 5, 7, 8, 11, 12}, 70] (* Jianing Song, Sep 22 2018 *) -
PARI
x='x+O('x^99); concat(0, Vec(x^2*(1+x)*(x^5+2*x^4-x^3+3*x^2-x+2)/((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2))) \\ Jianing Song, Sep 22 2018
Formula
G.f.: x^2*(x + 1)*(x^5 + 2*x^4 - x^3 + 3*x^2 - x + 2)/((x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x - 1)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jul 19 2016: (Start)
a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.
a(n) = (84*n - 84 - 9*(n mod 7) + 5*((n + 1) mod 7) - 2*((n + 2) mod 7) - 2*((n + 3) mod 7) + 5*((n + 4) mod 7) - 2*((n + 5) mod 7) + 5*((n + 6) mod 7))/49.
a(7k) = 12k - 1, a(7k-1) = 12k - 4, a(7k-2) = 12k - 5, a(7k-3) = 12k - 7, a(7k - 4) = 12k - 9, a(7k-5) = 12k - 10, a(7k-6) = 12k - 12. (End)
a(n) = a(n-7) + 12 for n > 7. - Jianing Song, Sep 22 2018
Comments