A046176 -id:A046176 - cp's OEIS frontend

A350986 a(0)=3, a(1)=105, a(2)=3567; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).

3, 105, 3567, 121173, 4116315, 139833537, 4750223943, 161367780525, 5481754313907, 186218278892313, 6325939728024735, 214895732473948677, 7300128964386230283, 247989489056657880945, 8424342498961981721847, 286179655475650720661853, 9721683943673162520781155, 330251074429411874985897417

Offset: 0

N. J. A. Sloane, Mar 08 2022

nonn

P.-F. Teilhet, Query 2376, L'Intermédiaire des Mathématiciens, 11 (1904), 138-139.

Index entries for linear recurrences with constant coefficients, signature (34,-1)

Cf. A001541, A001542, A350984, A002315, A001653, A350985.

Equals 3*A046176(n+1).

LinearRecurrence[{34,-1},{3,105},20] (* Harvey P. Dale, Mar 24 2023 *)

From Chai Wah Wu, Mar 08 2022: (Start)
a(n) = 34*a(n-1) - a(n-2) for n > 1.
G.f.: 3*(x + 1)/(x^2 - 34*x + 1). (End)

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

Original entry on oeis.org

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

Offset: 1

R. J. Mathar, Mar 14 2023

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

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).

Cf. A046176.

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

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)).

cp's OEIS Frontend

A350986 a(0)=3, a(1)=105, a(2)=3567; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).

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

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cp's OEIS Frontend

A350986 a(0)=3, a(1)=105, a(2)=3567; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).

Views

Author

Keywords

References

Links

Crossrefs

Programs

Mathematica

Formula

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

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

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