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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; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

Index entries for sequences related 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) with n>=2, a(-1)=0, a(0)=1, a(1)=13.

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

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

CROSSREFS

Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).

Sequence in context: A297454 A102146 A162768 * A163084 A163438 A163958

Adjacent sequences:  A097824 A097825 A097826 * A097828 A097829 A097830

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2004

STATUS

approved

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Last modified August 25 16:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)