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

1,3

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

Table of n, a(n) for n=1..107.

Wikipedia, Arabic scale

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

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

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 *)

Prog

(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

Crossrefs

Cf. A190785.

Sequence in context: A005556 A159698 A288931 * A228919 A047377 A188265

Adjacent sequences: A191273 A191274 A191275 * A191277 A191278 A191279

Keyword

nonn,easy

Author

Roberto Bertocco, May 29 2011

Status

approved