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A319279 Numbers that are congruent to {0, 3, 7, 10} mod 12.

%I A319279 #23 Sep 08 2022 08:46:23
%S A319279 0,3,7,10,12,15,19,22,24,27,31,34,36,39,43,46,48,51,55,58,60,63,67,70,
%T A319279 72,75,79,82,84,87,91,94,96,99,103,106,108,111,115,118,120,123,127,
%U A319279 130,132,135,139,142,144,147,151,154,156,159,163,166,168,171,175,178
%N A319279 Numbers that are congruent to {0, 3, 7, 10} mod 12.
%C A319279 Key-numbers of the pitches of a minor seventh chord on a standard chromatic keyboard, with root = 0.
%C A319279 Apart from the offset the same as A013574. - _R. J. Mathar_, Sep 27 2018
%H A319279 Jianing Song, <a href="/A319279/b319279.txt">Table of n, a(n) for n = 1..10000</a>
%H A319279 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%F A319279 a(n) = a(n-4) + 12 for n > 4.
%F A319279 a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.
%F A319279 G.f.: x^2*(3 + x + 2*x^2)/((x^2 + 1)*(x - 1)^2).
%F A319279 a(n) = (6*n - 5 + sqrt(2)*cos(Pi*n/2 + Pi/4))/2.
%F A319279 E.g.f.: ((6x - 5)*e^x + sqrt(2)*cos(x + Pi/4) + 4)/2.
%t A319279 Select[Range[0, 200], MemberQ[{0, 3, 7, 10}, Mod[#, 12]]&]
%t A319279 LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 7, 10, 12}, 100]
%o A319279 (Magma) [n : n in [0..150] | n mod 12 in [0, 3, 7, 10]]
%o A319279 (PARI) x='x+O('x^99); concat(0, Vec(x^2*(3+x+2*x^2)/((x^2+1)*(x-1)^2)))
%Y A319279 A guide for some sequences related to modes and chords:
%Y A319279 Modes:
%Y A319279 Lydian mode (F): A083089
%Y A319279 Ionian mode (C): A083026
%Y A319279 Mixolydian mode (G): A083120
%Y A319279 Dorian mode (D): A083033
%Y A319279 Aeolian mode (A): A060107 (raised seventh: A083028)
%Y A319279 Phrygian mode (E): A083034
%Y A319279 Locrian mode (B): A082977
%Y A319279 Third chords:
%Y A319279 Major chord (F,C,G): A083030
%Y A319279 Minor chord (D,A,E): A083031
%Y A319279 Diminished chord (B): A319451
%Y A319279 Seventh chords:
%Y A319279 Major seventh chord (F,C): A319280
%Y A319279 Dominant seventh chord (G): A083032
%Y A319279 Minor seventh chord (D,A,E): this sequence
%Y A319279 Half-diminished seventh chord (B): A319452
%K A319279 nonn,easy
%O A319279 1,2
%A A319279 _Jianing Song_, Sep 16 2018