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A244352
a(n) = Pell(n)^3 - Pell(n)^2, where Pell(n) is the n-th Pell number (A000129).
1
0, 0, 4, 100, 1584, 23548, 338100, 4798248, 67750848, 954701400, 13441659268, 189185124940, 2662308356400, 37463104912660, 527155118240244, 7417689205890000, 104375121328998144, 1468671237346368048, 20665783224031936900, 290789699203441908148
OFFSET
0,3
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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 26 2014
STATUS
approved