OFFSET
0,3
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 (7,-16).
FORMULA
a(n) = 2^(2n-1) sin(nA)/sqrt(15), where A is the angle opposite side BC in a triangle ABC having sidelengths |BC|=2, |CA| = 3, |AB| = 4 (the smallest integer-sided scalene triangle).
a(n) = 7 a(n-1) - 16 a(n-2), where a(0) = 1, a(1) = -1.
MATHEMATICA
(* Program 1 *)
A[a_, b_, c_] := ArcSin[Sqrt[1 - ((b^2 + c^2 - a^2)/(2 b c))^2]];
{a, b, c} = {2, 3, 4};
Table[TrigExpand[2^(3 n + 1) Sin[n A[b, c, a]]]/(3 Sqrt[15]), {n, 0, 30}]
(* Program 2 *)
LinearRecurrence[{11, -64}, {0, 1}, 30]
CROSSREFS
KEYWORD
sign,new
AUTHOR
Clark Kimberling, Sep 22 2024
STATUS
approved