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A099372 Squares of A099371(n) (generalized Fibonacci). 2
0, 1, 81, 6724, 558009, 46308025, 3843008064, 318923361289, 26466795978921, 2196425142889156, 182276820063821025, 15126779640154255921, 1255340433312739420416, 104178129185317217638609 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See the comment in A099279. This is example a=9.

LINKS

Table of n, a(n) for n=0..13.

Index entries for linear recurrences with constant coefficients, signature (82, 82, -1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= A099371(n)^2.

a(n)= 82*a(n-1) + 82*a(n-2) - a(n-3), n>=3; a(0)=0, a(1)=1, a(2)=81.

a(n)= 83*a(n-1) - a(n-2) - 2*(-1)^n, n>=2; a(0)=0, a(1)=1.

a(n)= 2*(T(n, 83/2)-(-1)^n)/85 with twice the Chebyshev's polynomials of the first kind: 2*T(n, 83/2)=A099373(n).

G.f.: x*(1-x)/((1-83*x+x^2)*(1+x)) = x*(1-x)/(1-82*x-82*x^2+x^3).

a(n)=-(2/85)*(-1)^n+(1/85)*[83/2+(9/2)*sqrt(85)]^n+(1/85)*[83/2-(9/2)*sqrt(85)]^n, with n>=0 [From Paolo P. Lava, Aug 28 2008]

CROSSREFS

Sequence in context: A217997 A089683 A183506 * A036515 A223553 A185770

Adjacent sequences:  A099369 A099370 A099371 * A099373 A099374 A099375

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 18 2004

STATUS

approved

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Last modified November 22 03:33 EST 2019. Contains 329384 sequences. (Running on oeis4.)