login
This site is supported by donations to The OEIS Foundation.

 

Logo

The submissions stack has been unacceptably high for several months now. Please voluntarily restrict your submissions and please help with the editing. (We don't want to have to impose further limits.)

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A097830 Partial sums of Chebyshev sequence S(n,16)= U(n,16/2)= A077412(n). 2
1, 17, 272, 4336, 69105, 1101345, 17552416, 279737312, 4458244577, 71052175921, 1132376570160, 18046972946640, 287619190576081, 4583860076270657, 73054142029754432, 1164282412399800256, 18555464456367049665 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..800

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (17, -17, 1).

FORMULA

a(n) = sum(S(k, 16), k=0..n) with S(k, 16) = U(k, 8) = A077412(k) Chebyshev's polynomials of the second kind.

G.f.: 1/((1-x)*(1-16*x+x^2)) = 1/(1-17*x+17*x^2-x^3).

a(n) = 17*a(n-1)-17*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=17.

a(n) = 16*a(n-1)-a(n-2)+1 with n>=1, a(-1)=0, a(0)=1.

a(n) = (S(n+1, 16) - S(n, 16) -1)/14.

MATHEMATICA

LinearRecurrence[{17, -17, 1}, {1, 17, 272}, 30] (* or *) Accumulate[ ChebyshevU[Range[0, 30], 8]] (* Harvey P. Dale, Nov 09 2011 *)

CROSSREFS

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

Sequence in context: A142898 A159678 A162803 * A163093 A163451 A163965

Adjacent sequences:  A097827 A097828 A097829 * A097831 A097832 A097833

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified August 28 05:09 EDT 2015. Contains 261118 sequences.