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A083120 Numbers that are congruent to {0, 2, 4, 5, 7, 9, 10} mod 12. 10
0, 2, 4, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 22, 24, 26, 28, 29, 31, 33, 34, 36, 38, 40, 41, 43, 45, 46, 48, 50, 52, 53, 55, 57, 58, 60, 62, 64, 65, 67, 69, 70, 72, 74, 76, 77, 79, 81, 82, 84, 86, 88, 89, 91, 93, 94, 96, 98, 100, 101, 103, 105, 106, 108, 110 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Key-numbers of the pitches of a Mixolydian mode scale on a standard chromatic keyboard, with root = 0. A Mixolydian mode scale can, for example, be played on consecutive white keys of a standard keyboard, starting on the root tone G.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).

FORMULA

G.f.: x^2*(2+2*x+x^2+2*x^3+2*x^4+x^5+2*x^6) / ( (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 - 77 + 5*(n mod 7) - 2*((n+1) mod 7) - 2*((n+2) mod 7) + 5*((n+3) mod 7) - 2*((n+4) mod 7) - 2*((n+5) mod 7) - 2*((n+6) mod 7))/49.

a(7k) = 12k-2, a(7k-1) = 12k-3, a(7k-2) = 12k-5, a(7k-3) = 12k-7, a(7k-4) = 12k-8, a(7k-5) = 12k-10, a(7k-6) = 12k-12. (End)

MAPLE

A083120:=n->12*floor(n/7)+[0, 2, 4, 5, 7, 9, 10][(n mod 7)+1]: seq(A083120(n), n=0..100); # Wesley Ivan Hurt, Jul 20 2016

MATHEMATICA

Select[Range[0, 120], MemberQ[{0, 2, 4, 5, 7, 9, 10}, Mod[#, 12]]&] (* Harvey P. Dale, Feb 20 2011 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 12 in [0, 2, 4, 5, 7, 9, 10]]; // Wesley Ivan Hurt, Jul 20 2016

(PARI) a(n)=[-2, 0, 2, 4, 5, 7, 9][n%7+1] + n\7*12 \\ Charles R Greathouse IV, Jul 21 2016

CROSSREFS

Cf. A083026, A083027, A083028, A083030, A083031, A083032, A083033, A083034, A082977, A083089.

Sequence in context: A121347 A106829 A190228 * A001614 A244222 A050731

Adjacent sequences:  A083117 A083118 A083119 * A083121 A083122 A083123

KEYWORD

nonn,easy,changed

AUTHOR

James Ingram (j.ingram(AT)t-online.de), Jun 01 2003

STATUS

approved

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Last modified July 28 22:23 EDT 2016. Contains 275149 sequences.