This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376283 #15 Oct 15 2024 10:31:24
%S A376283 1,24,-448,-59904,-2158592,-7766016,3080978432,160312590336,
%T A376283 2765438844928,-123759079981056,-10365137990975488,
%U A376283 -299512095597133824,2207640196898357248,585186082406535266304,24556707640476321185792,242424234892406990831616
%N 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.
%C A376283 If a prime p divides a term, then the indices n such that p divides a(n) comprise an arithmetic sequence; e.g., 7 divides a(4n+2) for n >= 0; 17 divides a(8n+4) for n>= 0. See the Renault paper in References.
%D A376283 Marc Renault, "The Period, Rank, and Order of the (a,b)-Fibonacci Sequence mod m", Math. Mag. 86 (2013) 372 - 380.
%H A376283 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (48,-1600).
%F 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.
%F A376283 a(n) = 48 a(n-1) - 1600 a(n-2), where a(0) = 1, a(1) = 24.
%F A376283 From _Stefano Spezia_, Oct 03 2024: (Start)
%F A376283 G.f.: (1 - 24*x)/(1 - 48*x + 1600*x^2).
%F A376283 E.g.f.: exp(24*x)*cos(32*x). (End)
%t A376283 (*Program 1*)
%t A376283 A[a_, b_, c_] := ArcCos[(b^2 + c^2 - a^2)/(2 b c)];
%t A376283 Table[TrigExpand[(20)^n Cos[n A[4, 5, 3]]], {n, 0, 30}]
%t A376283 (*Program 2*)
%t A376283 LinearRecurrence[{48, -1600}, {1, 24}, 30]
%Y A376283 Cf. A374880, A139030, A376285, A376455.
%K A376283 sign,easy
%O A376283 0,2
%A A376283 _Clark Kimberling_, Oct 02 2024