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A319452 Numbers that are congruent to {0, 3, 6, 10} mod 12. 4
0, 3, 6, 10, 12, 15, 18, 22, 24, 27, 30, 34, 36, 39, 42, 46, 48, 51, 54, 58, 60, 63, 66, 70, 72, 75, 78, 82, 84, 87, 90, 94, 96, 99, 102, 106, 108, 111, 114, 118, 120, 123, 126, 130, 132, 135, 138, 142, 144, 147, 150, 154, 156, 159, 162, 166, 168, 171, 174, 178 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-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 + 3*x + 4*x^2 + 2*x^3)/((1 + x)*(1 + x^2)*(1 - x)^2).

a(n) = (12*n - 11 + (-1)^n + 2*cos(Pi*n/2))/4.

E.g.f.: ((6*x - 5)*cosh(x) + (6*x - 6)*sinh(x) + cos(x) + 4)/2.

MATHEMATICA

Select[Range[0, 200], MemberQ[{0, 3, 6, 10}, Mod[#, 12]]&]

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 6, 10, 12}, 100]

PROG

(MAGMA) [n : n in [0..150] | n mod 12 in [0, 3, 6, 10]]

(PARI) x='x+O('x^99); concat(0, Vec(x^2*(3+3*x+4*x^2+2*x^3)/((1+x)*(1+x^2)*(1-x)^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): A319279

Half-diminished seventh chord (B): this sequence

Sequence in context: A310043 A316325 A114981 * A187744 A007960 A280243

Adjacent sequences:  A319449 A319450 A319451 * A319453 A319454 A319455

KEYWORD

nonn,easy

AUTHOR

Jianing Song, Sep 19 2018

STATUS

approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)