A376283 a(n) = (40)^n * cos(nB), where B is the angle opposite side CA in a triangle ABC having sidelengths |BC|=3, |CA|=4, |AB|=5; ABC is the smallest integer-sided right triangle.
1, 24, -448, -59904, -2158592, -7766016, 3080978432, 160312590336, 2765438844928, -123759079981056, -10365137990975488, -299512095597133824, 2207640196898357248, 585186082406535266304, 24556707640476321185792, 242424234892406990831616
Offset: 0
References
- Marc Renault, "The Period, Rank, and Order of the (a,b)-Fibonacci Sequence mod m", Math. Mag. 86 (2013) 372 - 380.
Links
- Index entries for linear recurrences with constant coefficients, signature (48,-1600).
Programs
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Mathematica
(*Program 1*) A[a_, b_, c_] := ArcCos[(b^2 + c^2 - a^2)/(2 b c)]; Table[TrigExpand[(20)^n Cos[n A[4, 5, 3]]], {n, 0, 30}] (*Program 2*) LinearRecurrence[{48, -1600}, {1, 24}, 30]
Formula
a(n) = (40)^n * cos(nB), where B is the angle opposite side CA in a triangle ABC having sidelengths |BC|=3, |CA|=4, |AB|=5; ABC is the smallest integer-sided right triangle.
a(n) = 48 a(n-1) - 1600 a(n-2), where a(0) = 1, a(1) = 24.
From Stefano Spezia, Oct 03 2024: (Start)
G.f.: (1 - 24*x)/(1 - 48*x + 1600*x^2).
E.g.f.: exp(24*x)*cos(32*x). (End)
Comments