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%I #28 Sep 10 2023 01:52:24
%S 1,3,4,6,8,9,11,13,15,16,18,20,21,23,25,27,28,30,32,33,35,37,39,40,42,
%T 44,45,47,49,51,52,54,56,57,59,61,63,64,66,68,69,71,73,75,76,78,80,81,
%U 83,85,87,88
%N Positions of white keys on piano keyboard, starting with A0 = the 1st key.
%H Robbert Fokkink, <a href="https://arxiv.org/abs/2309.01644">The Pell Tower and Ostronometry</a>, arXiv:2309.01644 [math.CO], 2023.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F a(n) = floor((12n-3)/7).
%F From _Chai Wah Wu_, Sep 11 2018: (Start)
%F a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.
%F G.f. for a keyboard with infinite number of keys: x*(x^7 + 2*x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^8 - x^7 - x + 1). (End)
%F a(n) = A060107(n) + 1 for 1 <= n <= 36. - _Jianing Song_, Oct 14 2019
%e First, 3rd, 4th, 6th, etc. keys of piano keyboard are white.
%t Join[{1,3},Flatten[Table[12n+{4,6,8,9,11,13,15},{n,0,6}]],{88}] (* _Harvey P. Dale_, Mar 15 2013 *)
%t LinearRecurrence[{1,0,0,0,0,0,1,-1},{1,3,4,6,8,9,11,13},52] (* _Harvey P. Dale_, May 14 2023 *)
%Y Cf. A059620, A081032, A060107.
%K fini,full,nonn
%O 1,2
%A _David W. Wilson_, Mar 02 2003
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