|
|
A083028
|
|
Numbers that are congruent to {0, 2, 3, 5, 7, 8, 11} mod 12.
|
|
17
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
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)
|
|
MAPLE
|
|
|
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:
Aeolian mode (A): A060107 (raised seventh: this sequence)
Chords:
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
James Ingram (j.ingram(AT)t-online.de), Jun 01 2003
|
|
STATUS
|
approved
|
|
|
|