OFFSET
1,2
COMMENTS
The key-numbers of the pitches of a minor scale on a standard chromatic keyboard, with root = 0 and raised seventh.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
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
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
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 *)
PROG
(Magma) [n : n in [0..150] | n mod 12 in [0, 2, 3, 5, 7, 8, 11]]; // Wesley Ivan Hurt, Jul 19 2016
(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
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
KEYWORD
nonn,easy
AUTHOR
James Ingram (j.ingram(AT)t-online.de), Jun 01 2003
STATUS
approved