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 A111567 Binomial transform of A048654: generalized Pellian with second term equal to 4. 6
 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; text; internal format)
 OFFSET 0,2 COMMENTS 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 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 A. S. Fraenkel, C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discr. Math. 126 (1-3) (1994) 137-149. [From R. J. Mathar, Aug 17 2009] Index entries for linear recurrences with constant coefficients, signature (4,-2). 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). From R. J. Mathar, Apr 02 2008: (Start) O.g.f.: (1+x)/(1-4*x+2*x^2). a(n) = A007070(n) + A007070(n-1). (End) 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 MATHEMATICA LinearRecurrence[{4, -2}, {1, 5}, 30] (* Harvey P. Dale, Jul 01 2016 *) 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'. (Maxima) a:1\$ a:5\$ a[n]:=4*a[n-1]-2*a[n-2]\$ A111567(n):=a[n]\$ makelist(A111567(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */ CROSSREFS Cf. A007052, A006012, A111566. Sequence in context: A255837 A122234 A113301 * A121050 A029869 A033453 Adjacent sequences:  A111564 A111565 A111566 * A111568 A111569 A111570 KEYWORD easy,nonn AUTHOR Creighton Dement, Aug 06 2005 EXTENSIONS Typo in definition corrected by Klaus Brockhaus, Aug 09 2009 STATUS approved

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Last modified October 7 08:00 EDT 2022. Contains 357270 sequences. (Running on oeis4.)