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A375881
a(n) = 2^(3n+1)*cos(nB), where B is the angle opposite side CA in a triangle ABC having sidelengths |BC|=2, |CA| = 3, |AB| = 4; ABC is the smallest integer-sided scalene triangle.
1
2, 11, -7, -781, -8143, -39589, 85673, 3476099, 32754017, 137823851, -580194727, -15202868461, -130099090543, -458106414469, 3287171235593, 65477694117539, 509875676214977, 1418060014842251, -17033383114493767, -278123055209335501, -1969217087975089423
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.
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
Cf. A375880.
Sequence in context: A368640 A290572 A220771 * A277055 A009258 A009204
KEYWORD
sign
AUTHOR
Clark Kimberling, Sep 11 2024
STATUS
approved