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A319279 Numbers that are congruent to {0, 3, 7, 10} mod 12. 5
0, 3, 7, 10, 12, 15, 19, 22, 24, 27, 31, 34, 36, 39, 43, 46, 48, 51, 55, 58, 60, 63, 67, 70, 72, 75, 79, 82, 84, 87, 91, 94, 96, 99, 103, 106, 108, 111, 115, 118, 120, 123, 127, 130, 132, 135, 139, 142, 144, 147, 151, 154, 156, 159, 163, 166, 168, 171, 175, 178 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Key-numbers of the pitches of a minor seventh chord on a standard chromatic keyboard, with root = 0.

Apart from the offset the same as A013574. - R. J. Mathar, Sep 27 2018

LINKS

Jianing Song, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

FORMULA

a(n) = a(n-4) + 12 for n > 4.

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.

G.f.: x^2*(3 + x + 2*x^2)/((x^2 + 1)*(x - 1)^2).

a(n) = (6*n - 5 + sqrt(2)*cos(Pi*n/2 + Pi/4))/2.

E.g.f.: ((6x - 5)*e^x + sqrt(2)*cos(x + Pi/4) + 4)/2.

MATHEMATICA

Select[Range[0, 200], MemberQ[{0, 3, 7, 10}, Mod[#, 12]]&]

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 7, 10, 12}, 100]

PROG

(MAGMA) [n : n in [0..150] | n mod 12 in [0, 3, 7, 10]]

(PARI) x='x+O('x^99); concat(0, Vec(x^2*(3+x+2*x^2)/((x^2+1)*(x-1)^2)))

CROSSREFS

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

Third chords:

Major chord (F,C,G): A083030

Minor chord (D,A,E): A083031

Diminished chord (B): A319451

Seventh chords:

Major seventh chord (F,C): A319280

Dominant seventh chord (G): A083032

Minor seventh chord (D,A,E): this sequence

Half-diminished seventh chord (B): A319452

Sequence in context: A105135 A225552 A147683 * A013574 A235915 A310178

Adjacent sequences:  A319276 A319277 A319278 * A319280 A319281 A319282

KEYWORD

nonn,easy

AUTHOR

Jianing Song, Sep 16 2018

STATUS

approved

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Last modified August 25 09:38 EDT 2019. Contains 326323 sequences. (Running on oeis4.)