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 A083031 Numbers that are congruent to {0, 3, 7} mod 12. 15
 0, 3, 7, 12, 15, 19, 24, 27, 31, 36, 39, 43, 48, 51, 55, 60, 63, 67, 72, 75, 79, 84, 87, 91, 96, 99, 103, 108, 111, 115, 120, 123, 127, 132, 135, 139, 144, 147, 151, 156, 159, 163, 168, 171, 175, 180, 183, 187, 192, 195, 199, 204, 207, 211, 216, 219 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Key-numbers of the pitches of a minor common chord on a standard chromatic keyboard, with root = 0. LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA G.f.: x^2*(3 + 4*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) = (12*n - 14 - cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3))/3. a(3k) = 12k - 5, a(3k-1) = 12k - 9, a(3k-2) = 12k - 12. (End) a(n) = a(n-3) + 12 for n > 3. - Jianing Song, Sep 22 2018 MAPLE A083031:=n->(12*n-14-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3: seq(A083031(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016 MATHEMATICA Select[Range[0, 400], MemberQ[{0, 3, 7}, Mod[#, 12]] &] (* Wesley Ivan Hurt, Jun 14 2016 *) LinearRecurrence[{1, 0, 1, -1}, {0, 3, 7, 12}, 100] (* Jianing Song, Sep 22 2018 *) PROG (MAGMA) [n : n in [0..300] | n mod 12 in [0, 3, 7]]; // Wesley Ivan Hurt, Jun 14 2016 (PARI) x='x+O('x^99); concat(0, Vec(x^2*(3+4*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: A083030 Minor chord: this sequence Dominant seventh chord: A083032 Sequence in context: A310227 A310228 A310229 * A189927 A189403 A022805 Adjacent sequences:  A083028 A083029 A083030 * A083032 A083033 A083034 KEYWORD nonn,easy AUTHOR James Ingram (j.ingram(AT)t-online.de), Jun 01 2003 STATUS approved

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Last modified September 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)