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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. [From 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).

O.g.f.: (1+x)/(1-4*x+2*x^2). a(n)=A007070(n)+A007070(n-1). - R. J. Mathar, 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]

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[0]:1$

a[1]: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 September 24 18:54 EDT 2017. Contains 292433 sequences.