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A099366 Squares of A005668(n) (generalized Fibonacci). 1
0, 1, 36, 1369, 51984, 1974025, 74960964, 2846542609, 108093658176, 4104712468081, 155870980128900, 5918992532430121, 224765845252215696, 8535183127051766329, 324112192982714904804, 12307728150216114616225 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See the comment in A099279. This is example a=6.

LINKS

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (37, 37, -1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n) = A005668(n)^2.

a(n) = 37*a(n-1) + 37*a(n-2) - a(n-3), n >= 3; a(0)=0, a(1)=1, a(2)=36.

a(n) = 38*a(n-1) - a(n-2) - 2*(-1)^n, n >= 2; a(0)=0, a(1)=1.

a(n) = (T(n, 19) - (-1)^n)/20 with the Chebyshev's polynomials of the first kind: T(n, 19) = A078986(n).

G.f.: x*(1-x)/((1 - 38*x + x^2)*(1+x)) = x*(1-x)/(1 - 37*x - 37*x^2 + x^3).

a(n) = -(1/20)*(-1)^n + (1/40)*(19-6*sqrt(10))^n + (1/40)*(19+6*sqrt(10))^n, with n >= 0. - Paolo P. Lava, Aug 27 2008

MAPLE

with (combinat):seq(fibonacci(n, 6)^2, n=0..15); # Zerinvary Lajos, Apr 09 2008

MATHEMATICA

LinearRecurrence[{37, 37, -1}, {0, 1, 36}, 20] (* Harvey P. Dale, Sep 23 2018 *)

CROSSREFS

Sequence in context: A226772 A158739 A218518 * A095657 A209014 A268897

Adjacent sequences:  A099363 A099364 A099365 * A099367 A099368 A099369

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 18 2004

STATUS

approved

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Last modified January 24 07:13 EST 2021. Contains 340398 sequences. (Running on oeis4.)