1,2

a(n) such that 9(T(a(n)-1)+ T(a(n+1)-1)) = 7(T(a(n)+a(n+1)-1)), where T(i) denotes the i-th triangular number.

Partial sums of Chebyshev sequence S(n,7)=U(n,7/2)= A004187(n+1).

Index entries for sequences related to Chebyshev polynomials.

G.f.: x/(1 - 8*x + 8*x^2 - x^3) = x/((1 - x)*(1 - 7*x + x^2)).

a(n)= 7*a(n-1) - a(n-2) + 1, n>=2, a(0):=0, a(1)=1.

a(n)= (S(n, 7)-S(n-1, 7) -1)/5, n>=1, with S(n, 7)=U(n, 7/2)= A004187(n+1).

a(n)=-1/5+(3/5)*[7/2-(3/2)*sqrt(5)]^n-(4/15)*[7/2-(3/2)*sqrt(5)]^n*sqrt(5)+(4/15)*sqrt(5)*[7/2 +(3/2)*sqrt(5)]^n+(3/5)*[7/2+(3/2)*sqrt(5)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jul 08 2008

a[1] = 1; a[2] = 8; a[3] = 56; a[n_] := a[n] = 8 a[n - 1] - 8 a[n - 2] + a[n - 3]; Table[ a[n], {n, 20}] (from Robert G. Wilson v Apr 08 2004)

Sequence in context: A003494 A057084 A101596 this_sequence A002914 A001666 A010556

Adjacent sequences: A092518 A092519 A092520 this_sequence A092522 A092523 A092524

nonn

K. S. Bhanu (bhanu_105(AT)yahoo.com) and M. N. Deshpande, Apr 06 2004

Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 08 2004

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