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Search: id:A111566
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| A111566 |
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a(n)=((1+sqrt8)(2+sqrt2)^n+(1-sqrt8)(2-sqrt2)^n)/2 |
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+0
3
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| 1, 6, 22, 76, 260, 888, 3032, 10352, 35344, 120672, 412000, 1406656, 4802624, 16397184, 55983488, 191139584, 652591360, 2228086272, 7607162368, 25972476928, 88675582976, 302757378048, 1033678346240, 3529198628864
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A048655: generalized Pellian with second term equal to 5.
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FORMULA
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a(n) = 4*a(n-1) - 2*a(n-2), a(0) = 1, a(1) = 6. Program "FAMP" returns: a(n) = A007052(n) - A006012(n) + A111567(n).
O.g.f.: (1+2*x)/(1-4*x+2*x^2). a(n)=A007070(n)+2*A007070(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2008
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP Code: 1vesseq[K*J] with K = + .5'i + .5'j + .5k' + .5'kk' and J = + .5i' + .5j' + 2'kk' + .5'ki' + .5'kj'.
(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+2*r)*(2+r)^n+(1-2*r)*(2-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 27 2009]
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CROSSREFS
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Cf. A007052, A006012, A111567.
Sequence in context: A027992 A159555 A032195 this_sequence A051945 A003699 A047124
Adjacent sequences: A111563 A111564 A111565 this_sequence A111567 A111568 A111569
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KEYWORD
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easy,nonn
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 06 2005
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EXTENSIONS
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Edited by N. J. A. Sloane, Jul 27 2009 using new definition from Al Hakanson (hawkuu(AT)gmail.com)
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