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

1,2

Links

Table of n, a(n) for n=1..52.

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).

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

Example

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

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 *)

Crossrefs

Cf. A059620, A081032, A060107.

Sequence in context: A330066 A047206 A187474 * A285681 A133280 A280762

Adjacent sequences: A081028 A081029 A081030 * A081032 A081033 A081034

Keyword

fini,full,nonn

Author

David W. Wilson, Mar 02 2003

Status

approved