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A375882
a(n) = 4^n cos(nC), where C is the angle opposite side AB in a triangle ABC having sidelengths |BC|=2, |CA| = 3, |AB| = 4; ABC is the smallest integer-sided scalene triangle.
1
1, -1, -14, 44, 136, -976, -224, 16064, -28544, -199936, 856576, 1485824, -16676864, 9580544, 247668736, -648626176, -2665447424, 15708913664, 11229331456, -273801281536, 367933259776, 3644953985024, -13176840126464, -31965583507456, 274760609038336
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.
FORMULA
a(n) = 4^n cos (nB), where C is angle opposite side AB in a triangle ABC having sidelengths |BC|=2, |CA|=3, |AB|=4 (the smallest integer-sided scalene triangle).
a(n) = -2 a(n-1) - 16 a(n-2), where a(0) = 1, a(1) = -1.
MATHEMATICA
(* Program 1 *)
A[a_, b_, c_] := ArcCos[(b^2 + c^2 - a^2)/(2 b c)];
Table[TrigExpand[4^n Cos[n A[4, 2, 3]]], {n, 0, 30}]
(* Program 2 *)
LinearRecurrence[{-2, -16}, {1, -1}, 30]
CROSSREFS
Cf. A375880.
Sequence in context: A009942 A031130 A215199 * A216258 A064348 A206215
KEYWORD
sign,easy
AUTHOR
Clark Kimberling, Sep 11 2024
STATUS
approved