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A098296
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Member r=11 of the family of Chebyshev sequences S_r(n) defined in A092184.
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3
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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; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to Chebyshev polynomials.
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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).
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=9*b-a+2; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 20 2011*)
LinearRecurrence[{10, -10, 1}, {0, 1, 11}, 30] (* From Harvey P. Dale, Jan 27 2012 *)
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CROSSREFS
| Sequence in context: A120655 A018203 A081906 * A037542 A037486 A103720
Adjacent sequences: A098293 A098294 A098295 * A098297 A098298 A098299
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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