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A191276 Numbers that are congruent to {0, 1, 4, 5, 7, 9, 11} mod 12. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)