login
Positions of black keys on piano keyboard, starting with A0 = the 1st key.
4

%I #22 Aug 10 2022 03:00:14

%S 2,5,7,10,12,14,17,19,22,24,26,29,31,34,36,38,41,43,46,48,50,53,55,58,

%T 60,62,65,67,70,72,74,77,79,82,84,86

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

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

%F From _Chai Wah Wu_, Sep 11 2018: (Start)

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

%F 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)

%F a(n) = A060106(n) + 1 for 1 <= n <= 36. - _Jianing Song_, Oct 14 2019

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

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

%Y Cf. A059620, A081031, A060106.

%K fini,full,nonn

%O 1,1

%A _David W. Wilson_, Mar 02 2003