A097828 - OEIS

%I #21 Jan 31 2026 10:14:22

%S 1,14,182,2353,30408,392952,5077969,65620646,847990430,10958254945,

%T 141609323856,1829962955184,23647909093537,305592855260798,

%U 3949059209296838,51032176865598097,659469240043478424,8522067943699621416,110127414028051599985,1423134314420971178390

%N Partial sums of Chebyshev sequence S(n,13)= U(n,13/2) = A078362(n).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-14,1).

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials</a>.

%F a(n) = Sum_{k=0..n} S(k, 13), with S(k, 13) = U(k, 13/2) = A078362(k) Chebyshev's polynomials of the second kind.

%F G.f.: 1/((1-x)*(1-13*x+x^2)) = 1/(1-14*x+14*x^2-x^3).

%F a(n) = 14*a(n-1)-14*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=14.

%F a(n) = 13*a(n-1)-a(n-2)+1 with n>=1, a(-1)=0, a(0)=1.

%F a(n) = (S(n+1, 13) - S(n, 13) - 1)/11.

%F Sum_{n>=0} 1/a(n) = (15 - sqrt(165))/2. - _Amiram Eldar_, Jan 31 2026

%t LinearRecurrence[{14, -14, 1}, {1, 14, 182}, 17] (* _Amiram Eldar_, Jan 31 2026 *)

%Y Cf. A078362.

%Y Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Aug 31 2004