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 A319279 Numbers that are congruent to {0, 3, 7, 10} mod 12. 5
 0, 3, 7, 10, 12, 15, 19, 22, 24, 27, 31, 34, 36, 39, 43, 46, 48, 51, 55, 58, 60, 63, 67, 70, 72, 75, 79, 82, 84, 87, 91, 94, 96, 99, 103, 106, 108, 111, 115, 118, 120, 123, 127, 130, 132, 135, 139, 142, 144, 147, 151, 154, 156, 159, 163, 166, 168, 171, 175, 178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Key-numbers of the pitches of a minor seventh chord on a standard chromatic keyboard, with root = 0. Apart from the offset the same as A013574. - _R. J. Mathar_, Sep 27 2018 LINKS Jianing Song, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-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 + x + 2*x^2)/((x^2 + 1)*(x - 1)^2). a(n) = (6*n - 5 + sqrt(2)*cos(Pi*n/2 + Pi/4))/2. E.g.f.: ((6x - 5)*e^x + sqrt(2)*cos(x + Pi/4) + 4)/2. MATHEMATICA Select[Range[0, 200], MemberQ[{0, 3, 7, 10}, Mod[#, 12]]&] LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 7, 10, 12}, 100] PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 3, 7, 10]] (PARI) x='x+O('x^99); concat(0, Vec(x^2*(3+x+2*x^2)/((x^2+1)*(x-1)^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): this sequence Half-diminished seventh chord (B): A319452 Sequence in context: A105135 A225552 A147683 * A013574 A235915 A310178 Adjacent sequences:  A319276 A319277 A319278 * A319280 A319281 A319282 KEYWORD nonn,easy AUTHOR _Jianing Song_, Sep 16 2018 STATUS approved

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Last modified February 20 13:56 EST 2020. Contains 332078 sequences. (Running on oeis4.)