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 A319452 Numbers that are congruent to {0, 3, 6, 10} mod 12. 4
 0, 3, 6, 10, 12, 15, 18, 22, 24, 27, 30, 34, 36, 39, 42, 46, 48, 51, 54, 58, 60, 63, 66, 70, 72, 75, 78, 82, 84, 87, 90, 94, 96, 99, 102, 106, 108, 111, 114, 118, 120, 123, 126, 130, 132, 135, 138, 142, 144, 147, 150, 154, 156, 159, 162, 166, 168, 171, 174, 178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Key-numbers of the pitches of a half-diminished 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*(3 + 3*x + 4*x^2 + 2*x^3)/((1 + x)*(1 + x^2)*(1 - x)^2). a(n) = (12*n - 11 + (-1)^n + 2*cos(Pi*n/2))/4. E.g.f.: ((6*x - 5)*cosh(x) + (6*x - 6)*sinh(x) + cos(x) + 4)/2. MATHEMATICA Select[Range[0, 200], MemberQ[{0, 3, 6, 10}, Mod[#, 12]]&] LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 6, 10, 12}, 100] PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 3, 6, 10]] (PARI) x='x+O('x^99); concat(0, Vec(x^2*(3+3*x+4*x^2+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): A319280 Dominant seventh chord (G): A083032 Minor seventh chord (D,A,E): A319279 Half-diminished seventh chord (B): this sequence Sequence in context: A310043 A316325 A114981 * A187744 A007960 A280243 Adjacent sequences:  A319449 A319450 A319451 * A319453 A319454 A319455 KEYWORD nonn,easy AUTHOR Jianing Song, Sep 19 2018 STATUS approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)