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 A319280 Numbers that are congruent to {0, 4, 7, 11} mod 12. 4
 0, 4, 7, 11, 12, 16, 19, 23, 24, 28, 31, 35, 36, 40, 43, 47, 48, 52, 55, 59, 60, 64, 67, 71, 72, 76, 79, 83, 84, 88, 91, 95, 96, 100, 103, 107, 108, 112, 115, 119, 120, 124, 127, 131, 132, 136, 139, 143, 144, 148, 151, 155, 156, 160, 163, 167, 168, 172, 175, 179 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Key-numbers of the pitches of a major seventh chord on a standard chromatic keyboard, with root = 0. LINKS Jianing Song, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-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*(4 + 3*x + 4*x^2 + x^3)/((1 + x)*(1 + x^2)*(1 - x)^2). a(n) = (6*n - 4 + (-1)^n + sqrt(2)*cos(Pi*n/2 + Pi/4))/2. E.g.f.: ((6*x - 3)*cosh(x) + (6*x - 5)*sinh(x) + sqrt(2)*cos(x + Pi/4) + 2)/2. MATHEMATICA Select[Range[0, 200], MemberQ[{0, 4, 7, 11}, Mod[#, 12]]&] LinearRecurrence[{1, 0, 0, 1, -1}, {0, 4, 7, 11, 12}, 100] PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 4, 7, 11]] (PARI) x='x+O('x^99); concat(0, Vec(x^2*(4+3*x+4*x^2+x^3)/((1+x)*(1+x^2)*(1-x)^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 Aeolian mode (A): A060107 (raised seventh: A083028) 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): this sequence Dominant seventh chord (G): A083032 Minor seventh chord (D,A,E): A319279 Half-diminished seventh chord (B): A319452 Sequence in context: A164888 A023985 A023979 * A214975 A310720 A310721 Adjacent sequences:  A319277 A319278 A319279 * A319281 A319282 A319283 KEYWORD nonn,easy AUTHOR Jianing Song, Sep 16 2018 STATUS approved

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)