A081032 Positions of black keys on piano keyboard, starting with A0 = the 1st key.

2, 5, 7, 10, 12, 14, 17, 19, 22, 24, 26, 29, 31, 34, 36, 38, 41, 43, 46, 48, 50, 53, 55, 58, 60, 62, 65, 67, 70, 72, 74, 77, 79, 82, 84, 86

Offset

1,1

Links

Table of n, a(n) for n=1..36.

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

Formula

a(n) = floor((12n+2)/5).

From Chai Wah Wu, Sep 11 2018: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

G.f. for a keyboard with an infinite number of keys: x*(2*x^4 + 3*x^3 + 2*x^2 + 3*x + 2)/(x^6 - x^5 - x + 1). (End)

a(n) = A060106(n) + 1 for 1 <= n <= 36. - Jianing Song, Oct 14 2019

Example

2nd, 5th, 7th, 10th, etc. keys of piano keyboard are black.

Mathematica

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {2, 5, 7, 10, 12, 14}, 36] (* Harvey P. Dale, Sep 15 2018 *)

Crossrefs

Cf. A059620, A081031, A060106.

Sequence in context: A285058 A212446 A195437 * A082845 A003153 A187475

Adjacent sequences: A081029 A081030 A081031 * A081033 A081034 A081035

Keyword

fini,full,nonn

Author

David W. Wilson, Mar 02 2003

Status

approved