A097832 - OEIS

A097832

Partial sums of Chebyshev sequence S(n,19) = U(n,19/2) = A078368(n).

1, 20, 380, 7201, 136440, 2585160, 48981601, 928065260, 17584258340, 333172843201, 6312699762480, 119608122643920, 2266241630472001, 42938982856324100, 813574432639685900, 15414975237297708001, 292070955076016766120, 5533933171207020848280, 104852659297857379351201

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (20,-20,1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n) = Sum_{k=0..n} S(k, 19), with S(k, 19) = U(k, 19/2) = A078368(k) Chebyshev's polynomials of the second kind.

G.f.: 1/((1-x)*(1-19*x+x^2)) = 1/(1-20*x+20*x^2-x^3).

a(n) = 20*a(n-1)-20*a(n-2)+a(n-3), n>=2, a(-1)=0, a(0)=1, a(1)=20.

a(n) = 19*a(n-1)-a(n-2)+1, n>=1, a(-1)=0, a(0)=1.