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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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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Dropping the leading 1, this becomes the 4th row of the 2-shuffle Phi_2(W(sqrt(2)) of the Fraenkel-Kimberling publication. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2009]
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LINKS
| A. S. Fraenkel, C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discr. Math. 126 (1-3) (1994) 137-149. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2009]
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FORMULA
| 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)=A007070(n)+A007070(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2008
a(n)=((2+sqrt18)*(2+sqrt2)^n)+(2-sqrt18)*(2-sqrt2)^n)/4 offset 0. [From Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009]
a(n)=((5+sqrt32)(2+sqrt2)^n+(5-sqrt32)(2-sqrt2)^n)/2 offset 0. [From Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009]
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PROG
| 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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CROSSREFS
| Cf. A007052, A006012, A111566.
Sequence in context: A062809 A122234 A113301 * A029869 A033453 A147535
Adjacent sequences: A111564 A111565 A111566 * A111568 A111569 A111570
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KEYWORD
| easy,nonn
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 06 2005
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EXTENSIONS
| Typo in definition corrected by Klaus Brockhaus, Aug 09 2009
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