A361491 Expansion of x*(1+38*x+x^2)/((1-x)*(x^2-34*x+1)).

1, 73, 2521, 85681, 2910673, 98877241, 3358915561, 114104251873, 3876185648161, 131676207785641, 4473114879063673, 151954229680379281, 5161970694253831921, 175355049374949906073, 5956909708054042974601, 202359575024462511230401, 6874268641123671338859073, 233522774223180363009978121

Offset: 1

Author

R. J. Mathar, Mar 14 2023

Keywords

• nonn
• easy

Comments

Indices i of Tetrahedral Numbers T(i) such that T(i)*T(2*i) is a perfect square. [Ulas]

Links

• Paolo Xausa, Table of n, a(n) for n = 1..500
• Maciej Ulas, On certain diophantine equations related to triangular and tetrahedral numbers, arXiv:0811.2477 [math.NT] (2008) , u_n in Theorem 5.6.
• Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

Crossrefs

Cf. A046176.

Programs

Mathematica

LinearRecurrence[{35, -35, 1}, {1, 73, 2521}, 20] (* Paolo Xausa, Jan 18 2024 *)

Formula

a(n) = 35*a(n-1) -35*a(n-2) +a(n-3).

a(n) = 17*a(n-1)+36*A046176(n-1)+20. [Ulas]

4*a(n) = -5+9*(A029547(n)-33*A029547(n-1)).