1,2

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.

Index entries for sequences related to Chebyshev polynomials.

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 (ppl(AT)spl.at), Jun 16 2008

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)

Cf. A092521.

Sequence in context: A009454 A004985 A057086 this_sequence A010579 A010576 A003952

Adjacent sequences: A092417 A092418 A092419 this_sequence A092421 A092422 A092423

nonn

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

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 05 2004

Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 31 2004