A060106 Numbers that are congruent to {1, 4, 6, 9, 11} mod 12. The ebony keys on a piano, starting with A0 = the 0th key.

1, 4, 6, 9, 11, 13, 16, 18, 21, 23, 25, 28, 30, 33, 35, 37, 40, 42, 45, 47, 49, 52, 54, 57, 59, 61, 64, 66, 69, 71, 73, 76, 78, 81, 83, 85, 88, 90, 93, 95, 97, 100, 102, 105, 107, 109, 112, 114, 117, 119, 121, 124, 126, 129, 131, 133, 136, 138, 141, 143, 145, 148

Offset

1,2

Comments

A piano sequence since if a(n) < 88 then A059620(a(n)) = 1.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

a(n) = a(n-5) + 12.

a(n) = A081032(n) - 1 for 1 <= n <= 36. - Jianing Song, Oct 14 2019

From Colin Barker, Oct 14 2019: (Start)

G.f.: x*(1 + 3*x + 2*x^2 + 3*x^3 + 2*x^4 + x^5) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).

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

(End)

Prog

(PARI) Vec(x*(1 + 3*x + 2*x^2 + 3*x^3 + 2*x^4 + x^5) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Oct 14 2019

Crossrefs

Cf. A059620, A081032. Complement of A060107.

Sequence in context: A190348 A189363 A189926 * A186222 A184814 A190001

Adjacent sequences: A060103 A060104 A060105 * A060107 A060108 A060109

Keyword

easy,nonn

Author

Henry Bottomley, Feb 27 2001

Status

approved