A083030 Numbers that are congruent to {0, 4, 7} mod 12.

0, 4, 7, 12, 16, 19, 24, 28, 31, 36, 40, 43, 48, 52, 55, 60, 64, 67, 72, 76, 79, 84, 88, 91, 96, 100, 103, 108, 112, 115, 120, 124, 127, 132, 136, 139, 144, 148, 151, 156, 160, 163, 168, 172, 175, 180, 184, 187, 192, 196, 199, 204, 208, 211, 216, 220

Offset

1,2

Comments

Key-numbers of the pitches of a major common chord on a standard chromatic keyboard, with root = 0.

Links

Table of n, a(n) for n=1..56.

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

Formula

G.f.: x^2*(4 + 3*x + 5*x^2)/((1 + x + x^2)*(1 - x)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 14 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.

a(n) = 4*n - (13 + 2*cos(2*n*Pi/3))/3.

a(3k) = 12k - 5, a(3k-1) = 12k - 8, a(3k-2) = 12k - 12. (End)

a(n) = a(n-3) + 12 for n > 3. - Jianing Song, Sep 22 2018

Maple

A083030:=n->4*n-(13+2*cos(2*n*Pi/3))/3: seq(A083030(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016

Mathematica

Select[Range[0, 250], MemberQ[{0, 4, 7}, Mod[#, 12]]&] (* Harvey P. Dale, Apr 17 2014 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 4, 7, 12}, 100] (* Jianing Song, Sep 22 2018 *)

Prog

(Magma) [n : n in [0..300] | n mod 12 in [0, 4, 7]]; // Wesley Ivan Hurt, Jun 14 2016
(PARI) my(x='x+O('x^99)); concat(0, Vec(x^2*(4+3*x+5*x^2)/((1+x+x^2)*(1-x)^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: A083028)

Phrygian mode (E): A083034

Locrian mode (B): A082977

Chords:

Major chord: this sequence

Minor chord: A083031

Dominant seventh chord: A083032

Sequence in context: A076295 A280101 A310779 * A310780 A285961 A310781

Adjacent sequences: A083027 A083028 A083029 * A083031 A083032 A083033

Keyword

nonn,easy

Author

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

Status

approved