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 A083089 Numbers that are congruent to {0, 2, 4, 6, 7, 9, 11} mod 12. 15
 0, 2, 4, 6, 7, 9, 11, 12, 14, 16, 18, 19, 21, 23, 24, 26, 28, 30, 31, 33, 35, 36, 38, 40, 42, 43, 45, 47, 48, 50, 52, 54, 55, 57, 59, 60, 62, 64, 66, 67, 69, 71, 72, 74, 76, 78, 79, 81, 83, 84, 86, 88, 90, 91, 93, 95, 96, 98, 100, 102, 103, 105, 107, 108, 110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Key-numbers of the pitches of a Lydian mode scale on a standard chromatic keyboard, with root = 0. A Lydian mode scale can, for example, be played on consecutive white keys of a standard keyboard, starting on the root tone F. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..2000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1). FORMULA G.f.: x^2*(x^4 + x^3 + 2)*(1 + x + x^2)/((x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x - 1)^2). - R. J. Mathar, Oct 08 2011 From Wesley Ivan Hurt, Jul 20 2016: (Start) a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8. a(n) = (84*n - 63 - 2*(n mod 7) - 2*((n + 1) mod 7) + 5*((n + 2) mod 7) - 2*((n + 3) mod 7) - 2*((n + 4) mod 7) - 2*((n + 5) mod 7) + 5*((n + 6) mod 7))/49. a(7k) = 12k - 1, a(7k - 1) = 12k - 3, a(7k-2) = 12k - 5, a(7k-3) = 12k - 6, a(7k-4) = 12k - 8, a(7k-5) = 12k - 10, a(7k-6) = 12k - 12. (End) a(n) = 2*n - 2 - floor(2*(n - 1)/7). - Wesley Ivan Hurt, Sep 29 2017 a(n) = a(n-7) + 12 for n > 7. - Jianing Song, Sep 22 2018 MAPLE A083089:=n->12*floor(n/7)+[0, 2, 4, 6, 7, 9, 11][(n mod 7)+1]: seq(A083089(n), n=0..100); # Wesley Ivan Hurt, Jul 20 2016 MATHEMATICA Select[Range[0, 200], MemberQ[{0, 2, 4, 6, 7, 9, 11}, Mod[#, 12]]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 4, 6, 7, 9, 11, 12}, 90] (* Harvey P. Dale, Mar 29 2016 *) PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 2, 4, 6, 7, 9, 11]]; // Wesley Ivan Hurt, Jul 20 2016 (PARI) a(n) = 2*(n-1)-2*(n-1)\7; \\ Altug Alkan, Sep 21 2018 (PARI) x='x+O('x^99); concat(0, Vec(x^2*(x^4+x^3+2)*(1+x+x^2)/((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2))) \\ Jianing Song, Sep 22 2018 CROSSREFS A guide for some sequences related to modes and chords: Modes: Lydian mode (F): this sequence 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: A083031 Dominant seventh chord: A083032 Sequence in context: A292654 A083088 A080755 * A136617 A275814 A285376 Adjacent sequences:  A083086 A083087 A083088 * A083090 A083091 A083092 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.)