OFFSET
1,3
COMMENTS
The key-numbers of the pitches of a major Neapolitan scale on a standard chromatic keyboard, with root = 0.
LINKS
Wikipedia, Neapolitan 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)^2*(1-x+x^2)*(1+x+x^2)/((1-x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, Mar 11 2012
From Wesley Ivan Hurt, Jul 21 2016: (Start)
a(n) = a(n-7) + 12 for n>7.
a(n) = (84*n - 84 - 2*(n mod 7) - 2*((n+1) mod 7) - 2*((n+2) mod 7) - 2*((n+3) mod 7) - 2*((n+4) mod 7) + 5*((n+5) mod 7) + 5*((n+6) mod 7))/49.
a(7k) = 12k-1, a(7k-1) = 12k-3, a(7k-2) = 12k-5, a(7k-3) = 12k-7, a(7k-4) = 12k-9, a(7k-5) = 12k-11, a(7k-6) = 12k-12. (End)
MAPLE
A191275:=n->12*floor(n/7)+[0, 1, 3, 5, 7, 9, 11][(n mod 7)+1]: seq(A191275(n), n=0..100); # Wesley Ivan Hurt, Jul 21 2016
MATHEMATICA
Select[Range[0, 120], MemberQ[{0, 1, 3, 5, 7, 9, 11}, Mod[#, 12]]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 5, 7, 9, 11, 12}, 70] (* Harvey P. Dale, Jul 06 2014 *)
PROG
(PARI) concat(0, Vec((1+x)^2*(1-x+x^2)*(1+x+x^2)/(1-x)^2/(1+x+x^2+x^3+x^4+x^5+x^6)+O(x^98))) \\ Charles R Greathouse IV, Mar 11 2012
(Magma) [n : n in [0..150] | n mod 12 in [0, 1, 3, 5, 7, 9, 11]]; // Wesley Ivan Hurt, Jul 21 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roberto Bertocco, May 29 2011
STATUS
approved