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A375883
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; ABC is the smallest integer-sided scalene triangle.
1
0, 1, 7, 33, 119, 305, 231, -3263, -26537, -133551, -510265, -1435039, -1881033, 9793393, 98650279, 533857665, 2158599191, 6568471697, 11441714823, -25003543391, -358092240905, -2106588992079, -9016647090073, -29411105757247, -61611386859561, 39297984099025
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) = 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[{7, -16}, {0, 1}, 30]
CROSSREFS
Cf. A375880.
Sequence in context: A131211 A213131 A100855 * A256860 A221036 A338232
KEYWORD
sign
AUTHOR
Clark Kimberling, Sep 22 2024
STATUS
approved