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
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'.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
A. S. Fraenkel and Clark 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) = ((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
(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
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Aug 06 2005
EXTENSIONS
Typo in definition corrected by Klaus Brockhaus, Aug 09 2009
STATUS
approved