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A092936 Area of n-th triple of hexagons around a triangle. 5
1, 9, 100, 1089, 11881, 129600, 1413721, 15421329, 168220900, 1835008569, 20016873361, 218350598400, 2381839709041, 25981886201049, 283418908502500, 3091626107326449, 33724468272088441, 367877524885646400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is the unsigned member r=-9 of the family of Chebyshev sequences S_r(n) defined in A092184: ((-1)^(n+1))*a(n) = S_{-9}(n), n>=0.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (10, 10, -1).

FORMULA

a(n) = 10*(a(n-1)+a(n-2)) - a(n-3).

G.f.: (1-x)*x/(1-10*x-10*x^2+x^3).

a(n) = ((3-sqrt(13))^n-(3+sqrt(13))^n)^2/(13*4^n).

a(n) = 2*(T(n, 11/2)-(-1)^n)/13 with twice the Chebyshev's polynomials of the first kind evaluated at x=11/2: 2*T(n, 11/2)=A057076(n)=((11+3*sqrt(13))^n + (11-3*sqrt(13))^n)/2^n. - Wolfdieter Lang, Oct 18 2004

EXAMPLE

a(5) = 10*(1089+100)-9 = 11881. From A006190, a(5) = (3*33+10)^2 = 11881.

MAPLE

seq(fibonacci(n, 3)^2, n=1..18); # Zerinvary Lajos, Apr 05 2008

MATHEMATICA

CoefficientList[Series[(1-x)*x/(1-10*x-10*x^2+x^3), {x, 0, 20}], x]

(CoefficientList[Series[x/(1-3*x-x^2), {x, 0, 20}], x])^2

Table[Round[((3+Sqrt[13])^n)^2/(13*4^n)], {n, 0, 20}]

LinearRecurrence[{10, 10, -1}, {1, 9, 100}, 18] (* Georg Fischer, Feb 22 2019 *)

PROG

(GAP) a:=[1, 9, 100];; for n in [4..18] do a[n]:=10*(a[n-1]+a[n-2])-a[n-3]; od; a; # Muniru A Asiru, Feb 20 2018

CROSSREFS

Equals (A006190)^2.

Cf. A005386, A006190.

Sequence in context: A027769 A266098 A065736 * A056002 A060150 A202833

Adjacent sequences:  A092933 A092934 A092935 * A092937 A092938 A092939

KEYWORD

easy,nonn

AUTHOR

Peter J. C. Moses, Apr 18 2004

STATUS

approved

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Last modified June 24 04:50 EDT 2021. Contains 345416 sequences. (Running on oeis4.)