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A097827 Partial sums of Chebyshev sequence S(n,12)= U(n,6)=A004191(n). 0
1, 13, 156, 1860, 22165, 264121, 3147288, 37503336, 446892745, 5325209605, 63455622516, 756142260588, 9010251504541, 107366875793905, 1279392258022320, 15245340220473936, 181664690387664913 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

LINKS

Index entries for sequences relate d to Chebyshev polynomials.

FORMULA

a(n)= sum(S(k, 12), k=0..n) with S(k, 12)=U(k, 6)=A004191(k) Chebyshev's polynomials of the second kind.

G.f.: 1/((1-x)*(1-12*x+x^2)) = 1/(1-13*x+13*x^2-x^3).

a(n)=13*a(n-1)-13*a(n-2)+a(n-3), n>=2, a(-1):=0, a(0)=1, a(1)=13.

a(n)=12*a(n-1)-a(n-2)+1, n>=1, a(-1):=0, a(0)=1.

a(n)=(S(n+1, 12) - S(n, 12) -1)/10.

CROSSREFS

Sequence in context: A192092 A102146 A162768 * A163084 A163438 A163958

Adjacent sequences:  A097824 A097825 A097826 * A097828 A097829 A097830

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 14 23:53 EST 2012. Contains 205689 sequences.