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A083120 Numbers that are congruent to {0, 2, 4, 5, 7, 9, 10} mod 12. 15
0, 2, 4, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 22, 24, 26, 28, 29, 31, 33, 34, 36, 38, 40, 41, 43, 45, 46, 48, 50, 52, 53, 55, 57, 58, 60, 62, 64, 65, 67, 69, 70, 72, 74, 76, 77, 79, 81, 82, 84, 86, 88, 89, 91, 93, 94, 96, 98, 100, 101, 103, 105, 106, 108, 110 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Key-numbers of the pitches of a Mixolydian mode scale on a standard chromatic keyboard, with root = 0. A Mixolydian mode scale can, for example, be played on consecutive white keys of a standard keyboard, starting on the root tone G.
LINKS
FORMULA
G.f.: x^2*(2 + 2*x + x^2 + 2*x^3 + 2*x^4 + x^5 + 2*x^6)/((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 20 2016: (Start)
a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.
a(n) = (84*n - 77 + 5*(n mod 7) - 2*((n + 1) mod 7) - 2*((n + 2) mod 7) + 5*((n + 3) mod 7) - 2*((n + 4) mod 7) - 2*((n + 5) mod 7) - 2*((n + 6) mod 7))/49.
a(7k) = 12k - 2, a(7k-1) = 12k - 3, a(7k-2) = 12k - 5, a(7k-3) = 12k - 7, a(7k-4) = 12k - 8, 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
a(n) = floor(4 * (3*n - 2) / 7). Federico Provvedi, Nov 06 2023
MAPLE
A083120:= n-> 12*floor((n-1)/7)+[0, 2, 4, 5, 7, 9, 10][((n-1) mod 7)+1]:
seq(A083120(n), n=1..100); # Wesley Ivan Hurt, Jul 20 2016
MATHEMATICA
Select[Range[0, 120], MemberQ[{0, 2, 4, 5, 7, 9, 10}, Mod[#, 12]]&] (* Harvey P. Dale, Feb 20 2011 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 4, 5, 7, 9, 10, 12}, 70] (* Jianing Song, Sep 22 2018 *)
Quotient[4 (3 # - 2), 7] & /@ Range[96] (* Federico Provvedi, Nov 06 2023 *)
PROG
(Magma) [n : n in [0..150] | n mod 12 in [0, 2, 4, 5, 7, 9, 10]]; // Wesley Ivan Hurt, Jul 20 2016
(PARI) a(n)=[-2, 0, 2, 4, 5, 7, 9][n%7+1] + n\7*12 \\ Charles R Greathouse IV, Jul 21 2016
(PARI) my(x='x+O('x^99)); concat(0, Vec(x^2*(2+2*x+x^2+2*x^3+2*x^4+x^5+2*x^6)/((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^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): this sequence
Dorian mode (D): A083033
Aeolian mode (A): A060107 (raised seventh: A083028)
Phrygian mode (E): A083034
Locrian mode (B): A082977
Chords:
Major chord: A083030
Minor chord: A083031
Dominant seventh chord: A083032
Sequence in context: A106829 A190228 A286667 * A001614 A284535 A244222
KEYWORD
nonn,easy
AUTHOR
James Ingram (j.ingram(AT)t-online.de), Jun 01 2003
STATUS
approved

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Last modified March 29 08:46 EDT 2024. Contains 371267 sequences. (Running on oeis4.)