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A098296 Member r=11 of the family of Chebyshev sequences S_r(n) defined in A092184. 4
0, 1, 11, 100, 891, 7921, 70400, 625681, 5560731, 49420900, 439227371, 3903625441, 34693401600, 308336988961, 2740339499051, 24354718502500, 216452127023451, 1923714424708561, 17096977695353600, 151949084833473841 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru, Polynomial sequences on quadratic curves, Integers, Vol. 15, 2015, #A38.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (10, -10, 1).

FORMULA

a(n) = 2*(T(n, 9/2)-1)/7 with twice Chebyshev's polynomials of the first kind evaluated at x=9/2: 2*T(n, 9/2) = A056918(n) = ((9 + sqrt(77))^n + (9 - sqrt(77))^n)/2^n.

a(n) = 9*a(n-1) - a(n-2) + 2, n >= 2, a(0)=0, a(1)=1.

a(n) = 10*a(n-1) - 10*a(n-2) + a(n-3), n >= 3, a(0)=0, a(1)=1, a(2)=11.

G.f.: x*(1+x)/((1-x)*(1-9*x+x^2)) = x*(1+x)/(1-10*x+10*x^2-x^3) (from the Stephan link, see A092184).

MATHEMATICA

LinearRecurrence[{10, -10, 1}, {0, 1, 11}, 30] (* Harvey P. Dale, Jan 27 2012 *)

PROG

(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1+x)/((1-x)*(1-9*x+x^2)))) \\ G. C. Greubel, May 24 2019

(MAGMA) I:=[0, 1, 11]; [n le 3 select I[n] else 10*Self(n-1)-10*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, May 24 2019

(Sage) (x*(1+x)/((1-x)*(1-9*x+x^2))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019

(GAP) a:=[0, 1, 11];; for n in [4..30] do a[n]:=10*a[n-1]-10*a[n-2]+ a[n-3]; od; a; # G. C. Greubel, May 24 2019

CROSSREFS

Sequence in context: A120655 A018203 A081906 * A037542 A037486 A103720

Adjacent sequences:  A098293 A098294 A098295 * A098297 A098298 A098299

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 18 2004

STATUS

approved

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Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)