OFFSET
1,3
COMMENTS
Terms are the key numbers of the pitches of an Enigmatic scale on a standard chromatic keyboard, with root = 0.
LINKS
Wikipedia, Enigmatic scale.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
FORMULA
G.f.: x^2*(1 + 3*x + 2*x^2 + 2*x^3 + 2*x^4 + x^5 + x^6)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Stefano Spezia, Dec 01 2021
a(n) = a(n-7) + 12 for n >= 8. - Michael S. Branicky, Dec 02 2021
MATHEMATICA
upto=200; Select[Range[0, upto], MemberQ[{0, 1, 4, 6, 8, 10, 11}, Mod[#, 12]]&] (* Paolo Xausa, Nov 30 2021 *)
nterms=100; LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 4, 6, 8, 10, 11, 12}, nterms] (* Paolo Xausa, Nov 30 2021 *)
PROG
(Python)
def a(n): return 12*((n-1)//7) + [0, 1, 4, 6, 8, 10, 11][(n-1)%7]
print([a(n) for n in range(1, 66)]) # Michael S. Branicky, Dec 02 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roberto Bertocco, Nov 26 2021
STATUS
approved