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
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
KEYWORD
nonn,easy
AUTHOR
Roberto Bertocco, May 29 2011
STATUS
approved