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A191275 Numbers that are congruent to {0, 1, 3, 5, 7, 9, 11} mod 12.

%I A191275 #24 Sep 08 2022 08:45:57
%S A191275 0,1,3,5,7,9,11,12,13,15,17,19,21,23,24,25,27,29,31,33,35,36,37,39,41,
%T A191275 43,45,47,48,49,51,53,55,57,59,60,61,63,65,67,69,71,72,73,75,77,79,81,
%U A191275 83,84,85,87,89,91,93,95,96,97,99,101,103,105,107,108,109,111
%N A191275 Numbers that are congruent to {0, 1, 3, 5, 7, 9, 11} mod 12.
%C A191275 The key-numbers of the pitches of a major Neapolitan scale on a standard chromatic keyboard, with root = 0.
%H A191275 Wikipedia, <a href="http://en.wikipedia.org/wiki/Neapolitan_scale">Neapolitan scale</a>
%H A191275 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A191275 a(n) = a(n-1) + a(n-7) - a(n-8) for n>8.
%F A191275 G.f.: x^2*(1+x)^2*(1-x+x^2)*(1+x+x^2)/((1-x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - _Colin Barker_, Mar 11 2012
%F A191275 From _Wesley Ivan Hurt_, Jul 21 2016: (Start)
%F A191275 a(n) = a(n-7) + 12 for n>7.
%F A191275 a(n) = (84*n - 84 - 2*(n mod 7) - 2*((n+1) mod 7) - 2*((n+2) mod 7) - 2*((n+3) mod 7) - 2*((n+4) mod 7) + 5*((n+5) mod 7) + 5*((n+6) mod 7))/49.
%F A191275 a(7k) = 12k-1, a(7k-1) = 12k-3, a(7k-2) = 12k-5, a(7k-3) = 12k-7, a(7k-4) = 12k-9, a(7k-5) = 12k-11, a(7k-6) = 12k-12. (End)
%p A191275 A191275:=n->12*floor(n/7)+[0, 1, 3, 5, 7, 9, 11][(n mod 7)+1]: seq(A191275(n), n=0..100); # _Wesley Ivan Hurt_, Jul 21 2016
%t A191275 Select[Range[0,120], MemberQ[{0,1,3,5,7,9,11}, Mod[#,12]]&] (* or *) LinearRecurrence[{1,0,0,0,0,0,1,-1}, {0,1,3,5,7,9,11,12}, 70] (* _Harvey P. Dale_, Jul 06 2014 *)
%o A191275 (PARI) concat(0,Vec((1+x)^2*(1-x+x^2)*(1+x+x^2)/(1-x)^2/(1+x+x^2+x^3+x^4+x^5+x^6)+O(x^98))) \\ _Charles R Greathouse IV_, Mar 11 2012
%o A191275 (Magma) [n : n in [0..150] | n mod 12 in [0, 1, 3, 5, 7, 9, 11]]; // _Wesley Ivan Hurt_, Jul 21 2016
%Y A191275 Cf. A190785.
%K A191275 nonn,easy
%O A191275 1,3
%A A191275 _Roberto Bertocco_, May 29 2011