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A092420 a(n+2) = 9a(n+1) - a(n) + 1, with a(1)=1, a(2)=10. 9
1, 10, 90, 801, 7120, 63280, 562401, 4998330, 44422570, 394804801, 3508820640, 31184580960, 277152408001, 2463187091050, 21891531411450, 194560595612001, 1729153829096560, 15367823866257040, 136581260967216801 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..19.

Index entries for sequences related to Chebyshev polynomials.

FORMULA

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

MATHEMATICA

a[1] = 1; a[2] = 10; a[n_] := a[n] = 9a[n - 1] - a[n - 2] + 1; Table[ a[n], {n, 20}] (* Robert G. Wilson v, Apr 05 2004 *)

CROSSREFS

Cf. A092521.

Sequence in context: A276020 A164552 A057086 * A010579 A010576 A162983

Adjacent sequences:  A092417 A092418 A092419 * A092421 A092422 A092423

KEYWORD

nonn

AUTHOR

M. N. Deshpande (dpratap_ngp(AT)sancharnet.in), Apr 04 2004

EXTENSIONS

More terms from Robert G. Wilson v, Apr 05 2004

Chebyshev comments from Wolfdieter Lang, Aug 31 2004

STATUS

approved

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Last modified November 14 22:17 EST 2019. Contains 329134 sequences. (Running on oeis4.)