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 A319451 Numbers that are congruent to {0, 3, 6} mod 12; a(n) = 3*floor(4*n/3). 4
 0, 3, 6, 12, 15, 18, 24, 27, 30, 36, 39, 42, 48, 51, 54, 60, 63, 66, 72, 75, 78, 84, 87, 90, 96, 99, 102, 108, 111, 114, 120, 123, 126, 132, 135, 138, 144, 147, 150, 156, 159, 162, 168, 171, 174, 180, 183, 186, 192, 195, 198, 204, 207, 210, 216, 219, 222, 228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Key-numbers of the pitches of a diminished chord on a standard chromatic keyboard, with root = 0. LINKS Jianing Song, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA a(n) = a(n-3) + 12 for n > 2. a(n) = a(n-1) + a(n-3) - a(n-4) for n > 3. G.f.: 3*(1 + x + 2*x^2)/((1 - x)*(1 - x^3)). a(n) = 3*A004773(n) = 3*(floor(n/3) + n). a(n) = 4*n - 1 + sin((Pi/3)*(2*n + 1))/sin(Pi/3). - Federico Provvedi, Oct 23 2018 E.g.f.: (3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/(3*exp(x/2)) - exp(x)*(1 - 4*x). - Franck Maminirina Ramaharo, Nov 27 2018 MAPLE seq(3*floor(4*n/3), n=0..60); # Muniru A Asiru, Oct 24 2018 MATHEMATICA Select[Range[0, 200], MemberQ[{0, 3, 6}, Mod[#, 12]]&] LinearRecurrence[{1, 0, 1, -1}, {0, 3, 6, 12}, 100] Table[4n-1+Sin[Pi/3(2n+1)]/Sin[Pi/3], {n, 0, 99}] (* Federico Provvedi, Oct 23 2018 *) PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 3, 6]] (PARI) a(n)=3*(4*n\3) (GAP) Filtered([0..230], n->n mod 12 = 0 or n mod 12 = 3 or n mod 12 = 6); # Muniru A Asiru, Oct 24 2018 (Python) for n in range(0, 60): print(3*int(4*n/3), end=", ") # Stefano Spezia, Dec 07 2018 CROSSREFS Cf. A004773, A047464. 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): this sequence 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): A319452 Sequence in context: A067759 A331068 A310122 * A256882 A191267 A145204 Adjacent sequences:  A319448 A319449 A319450 * A319452 A319453 A319454 KEYWORD nonn,easy AUTHOR Jianing Song, Sep 19 2018 STATUS approved

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)