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A111567
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Binomial transform of A048654: generalized Pellian with second term equal to 4.
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6
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1, 5, 18, 62, 212, 724, 2472, 8440, 28816, 98384, 335904, 1146848, 3915584, 13368640, 45643392, 155836288, 532058368, 1816560896, 6202126848, 21175385600, 72297288704, 246838383616, 842758957056, 2877359060992
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OFFSET
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0,2
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COMMENTS
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Dropping the leading 1, this becomes the 4th row of the 2-shuffle Phi_2(W(sqrt(2)) of the Fraenkel-Kimberling publication. - R. J. Mathar, Aug 17 2009
Floretion Algebra Multiplication Program, FAMP Code: 1lesseq[K*J] with K = + .5'i + .5'j + .5k' + .5'kk' and J = + .5i' + .5j' + 2'kk' + .5'ki' + .5'kj'.
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 2*a(n-2), a(0) = 1, a(1) = 5. Program "FAMP" returns: A111566(n) = A007052(n) - A006012(n) + a(n).
O.g.f.: (1+x)/(1-4*x+2*x^2).
a(n) = ((2+sqrt(18))*(2+sqrt(2))^n) + (2-sqrt(18))*(2-sqrt(2))^n)/4, offset 0. - Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
a(n) = ((5+sqrt(32))(2+sqrt(2))^n+(5-sqrt(32))(2-sqrt(2))^n)/2 offset 0. - Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
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MATHEMATICA
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LinearRecurrence[{4, -2}, {1, 5}, 30] (* Harvey P. Dale, Jul 01 2016 *)
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PROG
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(Maxima)
a[0]:1$
a[1]:5$
a[n]:=4*a[n-1]-2*a[n-2]$
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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