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A097833 Partial sums of Chebyshev sequence S(n,20)= U(n,10)=A075843(n+1). 0
1, 21, 420, 8380, 167181, 3335241, 66537640, 1327417560, 26481813561, 528308853661, 10539695259660, 210265596339540, 4194772231531141, 83685179034283281, 1669508808454134480, 33306490990048406320 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

LINKS

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= sum(S(k, 20), k=0..n) with S(k, 20)=U(k, 10)=A075843(k+1) Chebyshev's polynomials of the second kind.

G.f.: 1/((1-x)*(1-20*x+x^2)) = 1/(1-21*x+21*x^2-x^3).

a(n)=20*a(n-1)-a(n-2)+1, n>=1, a(-1):=0, a(0)=1.

a(n)= (S(n+1, 20) - S(n, 20) -1)/18.

a(n)=21*a(n-1)-21*a(n-2)+a(n-3), n>=2, a(-1):=0, a(0)=1, a(1)=21.

CROSSREFS

Sequence in context: A106656 A083043 A162807 * A163145 A163503 A163977

Adjacent sequences:  A097830 A097831 A097832 * A097834 A097835 A097836

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004

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Last modified February 17 03:45 EST 2012. Contains 205978 sequences.