1,3

a(n)=A001353(2n)/4. a(n) corresponds also to one-sixth the area of Fleenor-Heronian triangle with middle side A003500(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 15 2002

a(n) give all (nontrivial, integer) solutions of Pell equation b(n+1)^2 - 48*a(n+1)^2 = +1 with b(n+1)=A011943(n), n>=0.

Number of units of a(n) belongs to a periodic sequence: 0, 1, 4, 5, 6, 9.We conclude that a(n) and a(n+6) have the same number of units. [From Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 05 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

D. A. Benaron, personal communication.

E. K. Lloyd (E.K.Lloyd(AT)maths.soton.ac.uk), "The standard deviation of 1, 2, .., n, Pell's equation and rational triangles", preprint.

T. D. Noe, Table of n, a(n) for n=1..100

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = 14*a(n-1) - a(n-2). G.f.: (x^2)/(1-14*x+x^2).

a(n+1) ~ 1/24*sqrt(3)*(2 + sqrt(3))^(2*n) - Joe Keane (jgk(AT)jgk.org), May 15 2002

a(n+1) = S(n-1, 14), n>=0, with S(n, x) := U(n, x/2) Chebyshev's polynomials of the second kind. S(-1, x) := 0. See A049310.

a(n+1) = ((7+4*sqrt(3))^n - (7-4*sqrt(3))^n)/(8*sqrt(3)).

a(n+1) = sqrt((A011943(n)^2 - 1)/48), n>=0.

Chebyshev's polynomials U(n-2, x) evaluated at x=7.

4*a(n+1) + A046184(n) = A055793(n+2) + A098301(n+1) 4*a(n+1) + A098301(n+1) + A055793(n+2) = A046184(n+1) (4*a(n+1))^2 = A098301(2n+1) (conjectures) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Nov 02 2004

(4*a(n))^2 = A103974(n)^2 - A011922(n-1)^2. - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 06 2005

a(n) = 13*(a(n-1)+a(n-2))-a(n-3), a(n) = 15*(a(n-1)-a(n-2))+a(n-3). a(n)=14*a(n-1)-a(n-2). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 26 2007

lst={}; Do[AppendTo[lst, GegenbauerC[n, 1, 7]], {n, 0, 8^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]

sage: [lucas_number1(n, 14, 1) for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

Cf. A001353, A003500.

Cf. A011945, A067900.

Cf. A103974, A011922.

Sequence in context: A086946 A158530 A171319 this_sequence A171288 A001023 A067221

Adjacent sequences: A007652 A007653 A007654 this_sequence A007656 A007657 A007658

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002