OFFSET
0,1
COMMENTS
If a prime p divides a term, then the indices n such that p divides a(n) comprise an arithmetic sequence; see the Renault paper in References. For a guide to related sequences, see A375880.
LINKS
Marc Renault, The Period, Rank, and Order of the (a,b)-Fibonacci Sequence mod m, Math. Mag. 86 (2013) pp. 372-380.
Index entries for linear recurrences with constant coefficients, signature (11,-64).
FORMULA
a(n) = 2^(3 n + 1)*cos(nB), where B is angle opposite side CA in a triangle ABC having sidelengths |BC|=2, |CA|=3, |AB|=4 (the smallest integer-sided scalene triangle).
a(n) = 11 a(n-1) - 64 a(n-2), where a(0) = 2, a(1) = 11.
MATHEMATICA
(* Program 1 *)
A[a_, b_, c_] := ArcCos[(b^2 + c^2 - a^2)/(2 b c)];
Table[TrigExpand[2^(3 n + 1) Cos[n A[3, 4, 2]]], {n, 0, 30}]
(* Program 2 *)
LinearRecurrence[{11, -64}, {2, 11}, 30]
CROSSREFS
KEYWORD
sign
AUTHOR
Clark Kimberling, Sep 11 2024
STATUS
approved