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A098298 Member r=13 of the family of Chebyshev sequences S_r(n) defined in A092184. 1
0, 1, 13, 144, 1573, 17161, 187200, 2042041, 22275253, 242985744, 2650567933, 28913261521, 315395308800, 3440435135281, 37529391179293, 409382867836944, 4465682155027093, 48713120837461081, 531378647057044800, 5796451996790031721, 63229593317633304133 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Colin Barker, Table of n, a(n) for n = 0..950

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (12,-12,1).

FORMULA

a(n) = 2*(T(n, 11/2) - 1)/9 with twice Chebyshev's polynomials of the first kind evaluated at x=11/2: 2*T(n, 11/2) = A057076(n) = ((11 + sqrt(117))^n + (11 - sqrt(117))^n)/2^n.

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

a(n) = 12*a(n-1) - 12*a(n-2) + a(n-3), n >= 3, a(0)=0, a(1)=1, a(2)=13.

G.f.: x*(1+x)/((1-x)*(1-11*x+x^2)) = x*(1+x)/(1-12*x+12*x^2-x^3) (from the Stephan link, see A092184).

MATHEMATICA

LinearRecurrence[{12, -12, 1}, {0, 1, 13}, 30] (* Harvey P. Dale, May 11 2012 *)

RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == 11 a[n-1] - a[n-2] + 2}, a, {n, 30}] (* Vincenzo Librandi, Mar 06 2016 *)

PROG

(PARI) concat(0, Vec(x*(1+x)/((1-x)*(1-11*x+x^2)) + O(x^25))) \\ Colin Barker, Mar 06 2016

(MAGMA) [n le 2 select n-1 else 11*Self(n-1)- Self(n-2) + 2: n in [1..30]]; // Vincenzo Librandi, Mar 06 2016

(Sage) (x*(1+x)/((1-x)*(1-11*x+x^2))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019

(GAP) a:=[0, 1, 13];; for n in [4..30] do a[n]:=12*a[n-1]-12*a[n-2]+ a[n-3]; od; a; # G. C. Greubel, May 24 2019

CROSSREFS

Cf. A098296, A098297.

Sequence in context: A015672 A234601 A164825 * A045725 A072351 A134489

Adjacent sequences:  A098295 A098296 A098297 * A098299 A098300 A098301

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 18 2004

STATUS

approved

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Last modified August 26 05:23 EDT 2019. Contains 326328 sequences. (Running on oeis4.)