A191276 Numbers that are congruent to {0, 1, 4, 5, 7, 9, 11} mod 12.

0, 1, 4, 5, 7, 8, 11, 12, 13, 16, 17, 19, 20, 23, 24, 25, 28, 29, 31, 32, 35, 36, 37, 40, 41, 43, 44, 47, 48, 49, 52, 53, 55, 56, 59, 60, 61, 64, 65, 67, 68, 71, 72, 73, 76, 77, 79, 80, 83, 84, 85, 88, 89, 91, 92, 95, 96, 97, 100, 101, 103, 104, 107, 108, 109, 112, 113, 115, 116, 119, 120, 121, 124, 125, 127, 128, 131, 132, 133, 136, 137, 139, 140, 143, 144, 145, 148, 149, 151, 152, 155, 156, 157, 160, 161, 163, 164, 167, 168, 169, 172, 173, 175, 176, 179, 180, 181

Offset: 1

Author

Roberto Bertocco, May 29 2011

Keywords

• nonn
• easy

Comments

The key-numbers of the pitches of a double harmonic scale (note also as Arabic or Byzantine) on a standard chromatic keyboard, with root = 0.

Links

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

Crossrefs

Cf. A190785.

Programs

Mathematica

LinearRecurrence[{1,0,0,0,0,0,1,-1},{0,1,4,5,7,8,11,12},120] (* Harvey P. Dale, Mar 24 2019 *)

PARI

concat(0,Vec((1+x+x^2)*(1+2*x-2*x^2+2*x^3+x^4)/(1-x)^2/(1+x+x^2+x^3+x^4+x^5+x^6)+O(x^99))) \\ Charles R Greathouse IV, Mar 11 2012

Formula

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

G.f.: x^2*(1 + x + x^2)*(1 + 2x - 2x^2 + 2x^3 + x^4)/((1-x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, Mar 11 2012