A244352 a(n) = Pell(n)^3 - Pell(n)^2, where Pell(n) is the n-th Pell number (A000129).

0, 0, 4, 100, 1584, 23548, 338100, 4798248, 67750848, 954701400, 13441659268, 189185124940, 2662308356400, 37463104912660, 527155118240244, 7417689205890000, 104375121328998144, 1468671237346368048, 20665783224031936900, 290789699203441908148

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..800

Index entries for linear recurrences with constant coefficients, signature (17,-25,-223,-79,95,-7,-1).

Formula

a(n) = A110272(n) - A079291(n).

G.f.: 4*x^2*(1+8*x-4*x^2+3*x^3) / ((1+x)*(1-6*x+x^2)*(1+2*x-x^2)*(1-14*x-x^2)).

a(n) = A045991(A000129(n)). - Michel Marcus, Jun 26 2014

Example

a(3) = Pell(3)^3 - Pell(3)^2 = 5^3 - 5^2 = 100.

Mathematica

CoefficientList[Series[4*x^2*(3*x^3-4*x^2+8*x+1) / ((x+1)*(x^2-6*x+1)*(x^2-2*x-1)*(x^2+14*x-1)), {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 26 2014 *)

Prog

(PARI)
pell(n) = round(((1+sqrt(2))^n-(1-sqrt(2))^n)/(2*sqrt(2)))
vector(50, n, pell(n-1)^3-pell(n-1)^2)
(Magma)
Pell:= func< n | n eq 0 select 0 else Evaluate(DicksonSecond(n-1, -1), 2) >;
[Pell(n)^3 - Pell(n)^2: n in [0..40]]; // G. C. Greubel, Aug 20 2022
(SageMath)
def Pell(n): return lucas_number1(n, 2, -1)
[Pell(n)^3 -Pell(n)^2 for n in (0..40)] # G. C. Greubel, Aug 20 2022

Crossrefs

Cf. A000129, A079291, A110272.

Sequence in context: A017090 A029995 A365608 * A173987 A052144 A165518

Adjacent sequences: A244349 A244350 A244351 * A244353 A244354 A244355

Keyword

nonn,easy

Author

Colin Barker, Jun 26 2014

Status

approved