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A098297 Member r=12 of the family of Chebyshev sequences S_r(n) defined in A092184. 5
0, 1, 12, 121, 1200, 11881, 117612, 1164241, 11524800, 114083761, 1129312812, 11179044361, 110661130800, 1095432263641, 10843661505612, 107341182792481, 1062568166419200, 10518340481399521, 104120836647576012 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (11, -11, 1).

FORMULA

a(n) = (T(n, 5)-1)/4 with Chebyshev's polynomials of the first kind evaluated at x=5: T(n, 5) = A001079(n) = ((5 + 2*sqrt(6))^n + (5 - 2*sqrt(6))^n)/2.

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

a(n) = 11*a(n-1) - 11*a(n-2) + a(n-3), n >= 3, a(0)=0, a(1)=1, a(2)=12.

G.f.: x*(1+x)/((1-x)*(1-10*x+x^2)) = x*(1+x)/(1-11*x+11*x^2-x^3) (from the Stephan link, see A092184).

a(n) = A132596(n) / 2. - Peter Bala, Dec 31 2012

MATHEMATICA

LinearRecurrence[{11, -11, 1}, {0, 1, 12}, 30] (* G. C. Greubel, May 24 2019 *)

PROG

(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1+x)/((1-x)*(1-10*x+x^2)))) \\ G. C. Greubel, May 24 2019

(MAGMA) I:=[0, 1, 12]; [n le 3 select I[n] else 11*Self(n-1)-11*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, May 24 2019

(Sage) (x*(1+x)/((1-x)*(1-10*x+x^2))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019

(GAP) a:=[0, 1, 12];; for n in [4..30] do a[n]:=11*a[n-1]-11*a[n-2]+ a[n-3]; od; a; # G. C. Greubel, May 24 2019

CROSSREFS

Cf. A097784, A098296.

Sequence in context: A222634 A018204 A176779 * A037543 A214317 A037487

Adjacent sequences:  A098294 A098295 A098296 * A098298 A098299 A098300

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 18 2004

STATUS

approved

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Last modified September 22 16:41 EDT 2019. Contains 327311 sequences. (Running on oeis4.)