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
Examples
2nd, 5th, 7th, 10th, etc. keys of piano keyboard are black.
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
Programs
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Mathematica
LinearRecurrence[{1,0,0,0,1,-1},{2,5,7,10,12,14},36] (* Harvey P. Dale, Sep 15 2018 *)
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