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A098301 Member r=16 of the family of Chebyshev sequences S_r(n) defined in A092184. 11
0, 1, 16, 225, 3136, 43681, 608400, 8473921, 118026496, 1643897025, 22896531856, 318907548961, 4441809153600, 61866420601441, 861688079266576, 12001766689130625, 167163045568562176, 2328280871270739841, 32428769152221795600, 451674487259834398561 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also n such that (3*n^2 + n)/4 = n*(3*n + 1)/4 is a perfect square. - Ctibor O. Zizka, Oct 15 2010

Consequently A049451(k) is a square if and only if k = a(n). - Bruno Berselli, Oct 14 2011

LINKS

Colin Barker, Table of n, a(n) for n = 0..874

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (15,-15,1).

FORMULA

a(n) = (T(n, 7)-1)/6 with Chebyshev's polynomials of the first kind evaluated at x=7: T(n, 7) = A011943(n) = ((7 + 4*sqrt(3))^n + (7 - 4*sqrt(3))^n)/2; therefore: a(n) = ((7 + 4*sqrt(3))^n + (7 - 4*sqrt(3))^n - 2)/12.

a(n) = A001353(n)^2 = S(n-1, 4)^2 with Chebyshev's polynomials of the second kind evaluated at x=4, S(n, 4):=U(n, 2).

a(n) = 14*a(n-1) - a(n-2) + 2, n >= 2, a(0)=0, a(1)=1.

a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3), n >= 3.

G.f.: x*(1+x)/((1-x)*(1 - 14*x + x^2)) = x*(1+x)/(1 - 15*x + 15*x^2 - x^3) (from the Stephan link, see A092184).

Conjecture: 4*A007655(n+1) + A046184(n) = A055793(n+2) + a(n+1). - Creighton Dement, Nov 01 2004

a(n) = (A001075(n)^2-1)/3. - Parker Grootenhuis, Nov 28 2017

PROG

(PARI) concat(0, Vec(x*(1+x)/((1-x)*(1-14*x+x^2)) + O(x^50))) \\ Colin Barker, Jun 15 2015

CROSSREFS

Cf. A001075, A001353, A049451, A092184.

Sequence in context: A209444 A051822 A017438 * A014897 A048445 A028340

Adjacent sequences:  A098298 A098299 A098300 * A098302 A098303 A098304

KEYWORD

nonn,easy,changed

AUTHOR

Wolfdieter Lang, Oct 18 2004

STATUS

approved

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Last modified December 16 09:12 EST 2017. Contains 296087 sequences.