login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).

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

MAPLE

A083120:=n->12*floor(n/7)+[0, 2, 4, 5, 7, 9, 10][(n mod 7)+1]: seq(A083120(n), n=0..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 *)

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) 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

Adjacent sequences:  A083117 A083118 A083119 * A083121 A083122 A083123

KEYWORD

nonn,easy

AUTHOR

James Ingram (j.ingram(AT)t-online.de), Jun 01 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 16:00 EDT 2019. Contains 321292 sequences. (Running on oeis4.)