OFFSET
1,2
COMMENTS
Key-numbers of the pitches of a minor seventh chord on a standard chromatic keyboard, with root = 0.
Apart from the offset the same as A013574. - R. J. Mathar, Sep 27 2018
LINKS
Jianing Song, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
a(n) = a(n-4) + 12 for n > 4.
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.
G.f.: x^2*(3 + x + 2*x^2)/((x^2 + 1)*(x - 1)^2).
a(n) = (6*n - 5 + sqrt(2)*cos(Pi*n/2 + Pi/4))/2.
E.g.f.: ((6x - 5)*e^x + sqrt(2)*cos(x + Pi/4) + 4)/2.
MATHEMATICA
Select[Range[0, 200], MemberQ[{0, 3, 7, 10}, Mod[#, 12]]&]
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 7, 10, 12}, 100]
PROG
(Magma) [n : n in [0..150] | n mod 12 in [0, 3, 7, 10]]
(PARI) x='x+O('x^99); concat(0, Vec(x^2*(3+x+2*x^2)/((x^2+1)*(x-1)^2)))
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
Third chords:
Major chord (F,C,G): A083030
Minor chord (D,A,E): A083031
Diminished chord (B): A319451
Seventh chords:
Major seventh chord (F,C): A319280
Dominant seventh chord (G): A083032
Minor seventh chord (D,A,E): this sequence
Half-diminished seventh chord (B): A319452
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Sep 16 2018
STATUS
approved