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A098305 Unsigned member r=-5 of the family of Chebyshev sequences S_r(n) defined in A092184. 1
0, 1, 5, 36, 245, 1681, 11520, 78961, 541205, 3709476, 25425125, 174266401, 1194439680, 8186811361, 56113239845, 384605867556, 2636127833045, 18068288963761, 123841894913280, 848824975429201, 5817932933091125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

((-1)^(n+1))*a(n) = S_{-5}(n), n>=0, defined in A092184.

LINKS

Table of n, a(n) for n=0..20.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (6,6,-1).

FORMULA

a(n)= 2*(T(n, 7/2)-(-1)^n)/9, with twice the Chebyshev's polynomials of the first kind evaluated at x=7/2: 2*T(n, 7/2)=A056854(n)= ((7+sqrt(45))^n + (7-sqrt(45))^n)/2^n.

a(n)= 7*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.

a(n)= 6*a(n-1) + 6*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=5.

G.f.: x*(1-x)/((1+x)*(1-7*x+x^2)) = x*(1-x)/(1-6*x-6*x^2+x^3) (from the Stephan link, see A092184).

CROSSREFS

Sequence in context: A212329 A015547 A067376 * A055270 A297576 A164110

Adjacent sequences:  A098302 A098303 A098304 * A098306 A098307 A098308

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 18 2004

STATUS

approved

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)