

A097784


Partial sums of Chebyshev sequence S(n,10) = U(n,5) = A004189(n+1).


10



1, 11, 110, 1090, 10791, 106821, 1057420, 10467380, 103616381, 1025696431, 10153347930, 100507782870, 994924480771, 9848737024841, 97492445767640, 965075720651560, 9553264760747961, 94567571886828051, 936122454107532550, 9266656969188497450
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OFFSET

0,2


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
D. Fortin, Bspline Toeplitz Inverse Under Corner Perturbations, International Journal of Pure and Applied Mathematics, Volume 77, No. 1, 2012, 107118.  From N. J. A. Sloane, Oct 22 2012
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (11,11,1).


FORMULA

a(n) = Sum_{k=0..n} S(k, 10) with S(k, 10) = U(k, 5) = A004189(k+1) Chebyshev's polynomials of the second kind.
G.f.: 1/((1x)*(1  10*x + x^2)) = 1/(1  11*x + 11*x^2  x^3).
a(n) = 11*a(n1)  11*a(n2) + a(n3) with n >= 2, a(1)=0, a(0)=1, a(1)=11.
a(n) = 10*a(n1)  a(n2) + 1 with n >= 1, a(1)=0, a(0)=1.
a(n) = (S(n+1, 10)  S(n, 10)  1)/8.
a(n) = (6 + (2711*sqrt(6))*(5  2*sqrt(6))^n + (5 + 2*sqrt(6))^n*(27 + 11*sqrt(6)))/48.  Colin Barker, Mar 05 2016


MATHEMATICA

LinearRecurrence[{11, 11, 1}, {1, 11, 110}, 30] (* G. C. Greubel, May 24 2019 *)


PROG

(PARI) Vec(1/((1x)*(110*x+x^2)) + O(x^30)) \\ Colin Barker, Jun 14 2015
(MAGMA) I:=[1, 11, 110]; [n le 3 select I[n] else 11*Self(n1)11*Self(n2) +Self(n3): n in [1..30]]; // G. C. Greubel, May 24 2019
(Sage) (1/((1x)*(1  10*x + x^2))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019
(GAP) a:=[1, 11, 110];; for n in [4..30] do a[n]:=11*a[n1]11*a[n2]+ a[n3]; od; a; # G. C. Greubel, May 24 2019


CROSSREFS

Cf. A098296.
Cf. A212336 for more sequences with g.f. of the type 1/(1k*x+k*x^2x^3).
Sequence in context: A115822 A162760 A190871 * A121031 A115804 A162987
Adjacent sequences: A097781 A097782 A097783 * A097785 A097786 A097787


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Aug 31 2004


STATUS

approved



