A108741 Member r=100 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 100, 9801, 960400, 94109401, 9221760900, 903638458801, 88547347201600, 8676736387298001, 850231618608002500, 83314021887196947001, 8163923913326692803600, 799981229484128697805801, 78389996565531285692164900, 7681419682192581869134354401, 752700738858307491889474566400

Offset

0,3

Comments

Partial sums of A046173. [Joerg Arndt, Jun 10 2013]

Links

Table of n, a(n) for n=0..16.

Index entries for sequences related to Chebyshev polynomials.

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

Formula

a(n) = ((49+20*sqrt(6))^n+(49-20*sqrt(6))^n -2)/96 = 98*a(n-1)-a(n-2)+2 = 99*a(n-1)-99*a(n-2)+a(n-3) = (a(n-1)-1)^2/a(n-2) = A004189(n)^2.

G.f.: -x*(x+1)/((x-1)*(x^2-98*x+1)). [Colin Barker, Oct 24 2012]

From Wolfdieter Lang, Feb 01 2016: (Start)

a(n) = (T(n, 49) - 1)/48 = (T(2*n, 5) - 1)/48 with Chebyshev's T polynomials A053120. See the name.

a(n) = A000217((T(n, 5) - 1)/2)/3. n >= 0.

a(n) = S(n-1, 10)^2 = A004189(n)^2, with Chebyshev's S polynomials A049310. This is the triangular number = 3*square number identity. Cf. the famous triangular number = square number identity: A000217((T(n, 3) - 1)/2) = S(n-1, 6)^2. A001109 and A001110. (End)

Mathematica

LinearRecurrence[{99, -99, 1}, {0, 1, 100}, 20] (* Vincenzo Librandi, Feb 02 2016 *)

Prog

(Magma) I:=[0, 1, 100]; [n le 3 select I[n] else 99*Self(n-1)-99*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Feb 02 2016

Crossrefs

Cf. A000217, A004189.

Sequence in context: A260859 A117687 A262806 * A192937 A029798 A029775

Adjacent sequences: A108738 A108739 A108740 * A108742 A108743 A108744

Keyword

nonn,easy

Author

Henry Bottomley, Jun 22 2005

Status

approved