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A092420
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a(n+2)=9a(n+1)-a(n)+1, with a(1)=1, a(2)=10.
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9
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1, 10, 90, 801, 7120, 63280, 562401, 4998330, 44422570, 394804801, 3508820640, 31184580960, 277152408001, 2463187091050, 21891531411450, 194560595612001, 1729153829096560, 15367823866257040, 136581260967216801
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OFFSET
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1,2
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COMMENTS
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Let T(n) denote the n-th triangular number. If i, j are any two successive elements of the above sequence then (T(i-1)+T(j-1))/T(i+j-1)=9/11.
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LINKS
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Table of n, a(n) for n=1..19.
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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G.f.: x/(1-10*x+10*x^2-x^3) = x/((1-x)*(1 -9*x+x^2)).
a(n)= 10*a(n-1)-10*a(n-2)+a(n-3), n>=3, a(0):=0, a(1)=1, a(2)=10.
a(n)= (S(n, 9)-S(n-1, 9) -1)/7, n>=1.
a(n+1)= sum(S(n, 9), k=0..n), n>=0, with S(n, 9)=U(n, 9/2)=A018913(n+1). (Partial sums of Chebyshev sequence A018913 ).
a(n)=-1/7+(4/7)*[9/2+(1/2)*sqrt(77)]^n-(5/77)*[9/2-(1/2)*sqrt(77)]^n*sqrt(77)+(5/77)*[9/2+(1/2) *sqrt(77)]^n*sqrt(77)+(4/7)*[9/2-(1/2)*sqrt(77)]^n, with n>=0 - Paolo P. Lava, Jun 16 2008
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MATHEMATICA
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a[1] = 1; a[2] = 10; a[n_] := a[n] = 9a[n - 1] - a[n - 2] + 1; Table[ a[n], {n, 20}] (from Robert G. Wilson v Apr 05 2004)
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CROSSREFS
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Cf. A092521.
Sequence in context: A004985 A164552 A057086 * A010579 A010576 A162983
Adjacent sequences: A092417 A092418 A092419 * A092421 A092422 A092423
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KEYWORD
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nonn
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AUTHOR
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M. N. Deshpande (dpratap_ngp(AT)sancharnet.in), Apr 04 2004
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EXTENSIONS
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More terms from Robert G. Wilson v, Apr 05 2004
Chebyshev comments from Wolfdieter Lang, Aug 31 2004
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STATUS
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approved
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