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A098212
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Expansion of (5-x^2)/((1+x)*(1-6*x+x^2)).
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2
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5, 25, 149, 865, 5045, 29401, 171365, 998785, 5821349, 33929305, 197754485, 1152597601, 6717831125, 39154389145, 228208503749, 1330096633345, 7752371296325, 45184131144601, 263352415571285, 1534930362283105, 8946229758127349, 52142448186480985
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OFFSET
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0,1
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COMMENTS
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Old name was: Relates the squares of Pell numbers with the squares of the numerators of continued fraction convergents to sqrt(2).
Floretion Algebra Multiplication Program, FAMP Code: 1vesseq[(j' + k' + 'ii')*('j + 'k + 'ii')] - Creighton Dement, Aug 16 2005
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LINKS
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FORMULA
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G.f.: (5-x^2)/((1+x)*(1-6*x+x^2)).
a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3), a(0) = 5, a(1) = 25, a(2) = 149. - Robert G. Wilson v, Nov 05 2004
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MATHEMATICA
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a[0]= 5; a[1]= 25; a[2]= 149; a[n_]:= a[n]= 5 a[n-1] + 5 a[n-2] - a[n-3]; Table[ a[n], {n, 0, 40}] (* Robert G. Wilson v, Nov 05 2004 *)
CoefficientList[Series[(5-x^2)/((1+x)(1-6x+x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[{5, 5, -1}, {5, 25, 149}, 40] (* Harvey P. Dale, Jun 09 2011 *)
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PROG
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(Magma) I:=[5, 25, 149]; [n le 3 select I[n] else 5*Self(n-1)+5*Self(n-2)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 26 2015
(SageMath)
def Pell(n): return lucas_number1(n, 2, -1)
[4*Pell(n+1)^2 +(Pell(n+1) +Pell(n))^2 for n in (0..40)] # G. C. Greubel, Aug 20 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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