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 A083032 Numbers that are congruent to {0, 4, 7, 10} mod 12. 16
 0, 4, 7, 10, 12, 16, 19, 22, 24, 28, 31, 34, 36, 40, 43, 46, 48, 52, 55, 58, 60, 64, 67, 70, 72, 76, 79, 82, 84, 88, 91, 94, 96, 100, 103, 106, 108, 112, 115, 118, 120, 124, 127, 130, 132, 136, 139, 142, 144, 148, 151, 154, 156, 160, 163, 166, 168, 172 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Key-numbers of the pitches of a dominant seventh chord on a standard chromatic keyboard, with root = 0. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA G.f.: x^2*(4 + 3*x + 3*x^2 + 2*x^3)/((1 + x)*(1 + x^2)*(1 - x)^2). - R. J. Mathar, Oct 08 2011 From Wesley Ivan Hurt, May 19 2016: (Start) a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5. a(n) = (12*n - 9 + (-1)^n + (-1)^((n+1)/2) + (-1)^(-(n+1)/2))/4. (End) a(2k) = A016957(k-1) for k > 0, a(2k-1) = A272975(k). - Wesley Ivan Hurt, Jun 01 2016 E.g.f.: (4 - sin(x) + (6*x - 5)*sinh(x) + (6*x - 4)*cosh(x))/2. - Ilya Gutkovskiy, Jun 01 2016 From Jianing Song, Sep 22 2018: (Start) a(n) = (12*n - 9 + (-1)^n - 2*sin(n*Pi/2))/4. a(n) = a(n-4) + 12 for n > 4. (End) MAPLE A083032:=n->(12*n-9+(-1)^n+(-1)^((n+1)/2)+(-1)^(-(n+1)/2))/4: seq(A083032(n), n=1..100); # Wesley Ivan Hurt, May 19 2016 MATHEMATICA Select[Range[0, 200], MemberQ[{0, 4, 7, 10}, Mod[#, 12]]&] (* Harvey P. Dale, Sep 13 2011 *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 4, 7, 10, 12}, 100] (* G. C. Greubel, Jun 01 2016 *) PROG (MAGMA) [(12*n-9+(-1)^n+(-1)^((n+1) div 2)+(-1)^(-(n+1) div 2))/4: n in [1..100]]; // Wesley Ivan Hurt, May 19 2016 (PARI) x='x+O('x^99); concat(0, Vec(x^2*(4+3*x+3*x^2+2*x^3)/((1+x)*(1+x^2)*(1-x)^2))) \\ Altug Alkan, Sep 21 2018 (GAP) Filtered([0..200], n-> n mod 12=0 or n mod 12=4 or n mod 12=7 or n mod 12=10); # Muniru A Asiru, Sep 22 2018 CROSSREFS Bisections: A016957, A272975. 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 Chords: Major chord: A083030 Minor chord: A083031 Dominant seventh chord: this sequence Sequence in context: A310676 A320929 A104280 * A284933 A020965 A065713 Adjacent sequences:  A083029 A083030 A083031 * A083033 A083034 A083035 KEYWORD nonn,easy AUTHOR James Ingram (j.ingram(AT)t-online.de), Jun 01 2003 STATUS approved

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Last modified May 27 17:53 EDT 2020. Contains 334664 sequences. (Running on oeis4.)