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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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1
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5, 25, 149, 865, 5045, 29401, 171365, 998785, 5821349, 33929305, 197754485, 1152597601, 6717831125, 39154389145, 228208503749, 1330096633345, 7752371296325, 45184131144601, 263352415571285, 1534930362283105
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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).
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LINKS
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Table of n, a(n) for n=0..19.
Index to sequences with linear recurrences with constant coefficients, signature (5,5,-1)
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FORMULA
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a(n) = 4*A079291(n+1) + A090390(n+1) = 4(A000129(n+1))^2 + (A001333(n+1))^2.
a(n) + a(n+1) = A075848(n+2) - A075848(n+1).
a(n) = A001541(n+1) + 2*A079291(n+1). - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 26 2004
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
a(n)=(1/2)*(-1)^n -(3/2)*sqrt(2)*{[3-2*sqrt(2)]^n-[3+2*sqrt(2)]^n} +(9/4)*{[3+2*sqrt(2)]^n+[3-2*sqrt(2)]^n}, with n>=0 [From Paolo P. Lava, Nov 28 2008]
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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, 20}] (from Robert G. Wilson v, Nov 05 2004)
CoefficientList[Series[(5-x^2)/((1+x)(1-6x+x^2)), {x, 0, 20}], x] (* or *) LinearRecurrence[{5, 5, -1}, {5, 25, 149}, 20] (* From Harvey P. Dale, Jun 09 2011 *)
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PROG
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(Floretion Algebra Multiplication Program, FAMP)
1vesseq[(j' + k' + 'ii')*('j + 'k + 'ii')] - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 16 2005
(PARI) Vec((5-x^2)/((1+x)*(1-6*x+x^2))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
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CROSSREFS
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Cf. A079291, A090390, A000129, A001333.
Sequence in context: A049427 A121639 A098349 * A002050 A047782 A106565
Adjacent sequences: A098209 A098210 A098211 * A098213 A098214 A098215
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KEYWORD
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nonn,easy
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 25 2004
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EXTENSIONS
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More terms from Robert G. Wilson v, Nov 05 2004
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STATUS
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approved
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