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A099367 Squares of A054413(n-1), n>=1,(generalized Fibonacci). 1
0, 1, 49, 2500, 127449, 6497401, 331240000, 16886742601, 860892632649, 43888637522500, 2237459621014849, 114066552034234801, 5815156694124960000, 296458924848338725201, 15113590010571150025249, 770496631614280312562500 (list; graph; refs; listen; history; internal format)
OFFSET

0,3

COMMENTS

See the comment in A099279. This is example a=7.

LINKS

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= A054413(n-1)^2, n>=1. a(0)=0.

a(n)= 50*a(n-1) + 50*a(n-2) - a(n-3), n>=3; a(0)=0, a(1)=1, a(2)=49.

a(n)= 51*a(n-1) - a(n-2) - 2*(-1)^n, n>=2; a(0)=0, a(1)=1.

a(n)= 2*(T(n, 51/2)-(-1)^n)/53 with twice the Chebyshev's polynomials of the first kind: 2*T(n, 51/2)=A099368(n).

G.f.: x*(1-x)/((1-51*x+x^2)*(1+x)) = x*(1-x)/(1-50*x-50*x^2+x^3).

a(n)=-(2/53)*(-1)^n+(1/53)*[51/2-(7/2)*sqrt(53)]^n+(1/53)*[51/2+(7/2)*sqrt(53)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Aug 28 2008]

CROSSREFS

Sequence in context: A087752 A069741 A203384 * A123841 A014773 A132539

Adjacent sequences:  A099364 A099365 A099366 * A099368 A099369 A099370

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004

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Last modified February 14 11:36 EST 2012. Contains 205623 sequences.