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A098298
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Member r=13 of the family of Chebyshev sequences S_r(n) defined in A092184.
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0
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0, 1, 13, 144, 1573, 17161, 187200, 2042041, 22275253, 242985744, 2650567933, 28913261521, 315395308800, 3440435135281, 37529391179293, 409382867836944, 4465682155027093, 48713120837461081, 531378647057044800
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..18.
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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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).
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MATHEMATICA
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Join[{a=0, b=1}, Table[c=11*b-a+2; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 20 2011*)
LinearRecurrence[{12, -12, 1}, {0, 1, 13}, 30] (* From Harvey P. Dale, May 11 2012 *)
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CROSSREFS
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Cf. A098296, A098297.
Sequence in context: A221103 A029483 A015672 * A045725 A072351 A134489
Adjacent sequences: A098295 A098296 A098297 * A098299 A098300 A098301
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Oct 18 2004
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STATUS
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approved
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