cp's OEIS Frontend

A083030 Numbers that are congruent to {0, 4, 7} mod 12.

%I A083030 #30 Sep 08 2022 08:45:10
%S A083030 0,4,7,12,16,19,24,28,31,36,40,43,48,52,55,60,64,67,72,76,79,84,88,91,
%T A083030 96,100,103,108,112,115,120,124,127,132,136,139,144,148,151,156,160,
%U A083030 163,168,172,175,180,184,187,192,196,199,204,208,211,216,220
%N A083030 Numbers that are congruent to {0, 4, 7} mod 12.
%C A083030 Key-numbers of the pitches of a major common chord on a standard chromatic keyboard, with root = 0.
%H A083030 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A083030 G.f.: x^2*(4 + 3*x + 5*x^2)/((1 + x + x^2)*(1 - x)^2). - _R. J. Mathar_, Oct 08 2011
%F A083030 From _Wesley Ivan Hurt_, Jun 14 2016: (Start)
%F A083030 a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.
%F A083030 a(n) = 4*n - (13 + 2*cos(2*n*Pi/3))/3.
%F A083030 a(3k) = 12k - 5, a(3k-1) = 12k - 8, a(3k-2) = 12k - 12. (End)
%F A083030 a(n) = a(n-3) + 12 for n > 3. - _Jianing Song_, Sep 22 2018
%p A083030 A083030:=n->4*n-(13+2*cos(2*n*Pi/3))/3: seq(A083030(n), n=1..100); # _Wesley Ivan Hurt_, Jun 14 2016
%t A083030 Select[Range[0,250], MemberQ[{0,4,7}, Mod[#,12]]&] (* _Harvey P. Dale_, Apr 17 2014 *)
%t A083030 LinearRecurrence[{1, 0, 1, -1}, {0, 4, 7, 12}, 100] (* _Jianing Song_, Sep 22 2018 *)
%o A083030 (Magma) [n : n in [0..300] | n mod 12 in [0, 4, 7]]; // _Wesley Ivan Hurt_, Jun 14 2016
%o A083030 (PARI) my(x='x+O('x^99)); concat(0, Vec(x^2*(4+3*x+5*x^2)/((1+x+x^2)*(1-x)^2))) \\ _Jianing Song_, Sep 22 2018
%Y A083030 A guide for some sequences related to modes and chords:
%Y A083030 Modes:
%Y A083030 Lydian mode (F): A083089
%Y A083030 Ionian mode (C): A083026
%Y A083030 Mixolydian mode (G): A083120
%Y A083030 Dorian mode (D): A083033
%Y A083030 Aeolian mode (A): A060107 (raised seventh: A083028)
%Y A083030 Phrygian mode (E): A083034
%Y A083030 Locrian mode (B): A082977
%Y A083030 Chords:
%Y A083030 Major chord: this sequence
%Y A083030 Minor chord: A083031
%Y A083030 Dominant seventh chord: A083032
%K A083030 nonn,easy
%O A083030 1,2
%A A083030 James Ingram (j.ingram(AT)t-online.de), Jun 01 2003