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A097826
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Partial sums of Chebyshev sequence S(n,11)= U(n,11/2)= A004190(n).
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5
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1, 12, 132, 1441, 15720, 171480, 1870561, 20404692, 222581052, 2427986881, 26485274640, 288910034160, 3151525101121, 34377866078172, 375005001758772, 4090677153268321, 44622443684192760, 486756203372852040
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Index entries for sequences relate d to Chebyshev polynomials.
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FORMULA
| a(n)= sum(S(k, 11), k=0..n) with S(k, 11)=U(k, 11/2)=A004190(k) Chebyshev's polynomials of the second kind.
G.f.: 1/((1-x)*(1-11*x+x^2)) = 1/(1-12*x+12*x^2-x^3).
a(n)=12*a(n-1)-12*a(n-2)+a(n-3), n>=2, a(-1):=0, a(0)=1, a(1)=12.
a(n)=11*a(n-1)-a(n-2)+1, n>=1, a(-1):=0, a(0)=1.
a(n)=(S(n+1, 11) - S(n, 11) -1)/9.
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MATHEMATICA
| Join[{a=1, b=12}, Table[c=11*b-a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 20 2011*)
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CROSSREFS
| Cf. A076765, A097784.
Sequence in context: A001336 A118475 A190873 * A010580 A010577 A163055
Adjacent sequences: A097823 A097824 A097825 * A097827 A097828 A097829
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
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