A173115 a(n) = -(sin(2*n*arccos(sqrt(3))))^2.

0, 24, 2400, 235224, 23049600, 2258625624, 221322261600, 21687323011224, 2125136332838400, 208241673295152024, 20405558846592060000, 1999536525292726728024, 195934173919840627286400

Offset: 0

Author

Artur Jasinski, Feb 10 2010

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (99,-99,1)

Crossrefs

Cf. A001079, A108741, A132592, A146311, A146312, A146313.

Programs

Mathematica

Table[ -Round[N[Sin[2 n ArcCos[Sqrt[3]]]^2, 100]], {n, 0, 20}]
OR
Table[Round[N[ -1/2 + (1/4) (49 + 20 Sqrt[6])^n + (1/4) (49 - 20 Sqrt[6])^n]], {n, 0, 6}]
OR
Clear[a]; a[n_] := a[n] = 99 a[n - 1] - 99 a[n - 2] + a[n - 3]; a[0] = 0; a[1] = 24; a[2] = 2400; Table[a[n], {n, 0, 10}]

PARI

a(n)=([0,1,0;0,0,1;1,-99,99]^n*[0;24;2400])[1,1] \\ Charles R Greathouse IV, Jun 11 2015

Formula

a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3), n > 2.

Binet formula: a(n) = -1/2 + (1/4)(49 + 20*sqrt(6))^n + (1/4)(49 - 20*sqrt(6))^n.

a(n) = 24*A108741(n).

From R. J. Mathar, Aug 23 2012: (Start)

G.f.: -24*x*(1+x) / ( (x-1)*(x^2-98*x+1) ).

a(n) = A132596(2n). (End)