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

Author

Henry Bottomley, Feb 27 2001

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A059620, A081032. Complement of A060107.

Programs

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

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)