A081031 Positions of white keys on piano keyboard, starting with A0 = the 1st key.

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, 44, 45, 47, 49, 51, 52, 54, 56, 57, 59, 61, 63, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 81, 83, 85, 87, 88

Offset: 1

Author

David W. Wilson, Mar 02 2003

Keywords

• fini
• full
• nonn

Examples

			First, 3rd, 4th, 6th, etc. keys of piano keyboard are white.
		

Links

• Robbert Fokkink, The Pell Tower and Ostronometry, arXiv:2309.01644 [math.CO], 2023.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).

Crossrefs

Cf. A059620, A081032, A060107.

Programs

Mathematica

Join[{1,3},Flatten[Table[12n+{4,6,8,9,11,13,15},{n,0,6}]],{88}] (* Harvey P. Dale, Mar 15 2013 *)
LinearRecurrence[{1,0,0,0,0,0,1,-1},{1,3,4,6,8,9,11,13},52] (* Harvey P. Dale, May 14 2023 *)

Formula

a(n) = floor((12n-3)/7).

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

a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.

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)

a(n) = A060107(n) + 1 for 1 <= n <= 36. - Jianing Song, Oct 14 2019