OFFSET
0,2
COMMENTS
Binomial transform of A048655: generalized Pellian with second term equal to 5.
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'.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
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) = 6.
From R. J. Mathar, Apr 02 2008: (Start)
O.g.f.: (1+2*x)/(1-4*x+2*x^2).
a(n) = Sum_{k=0..n} A207543(n,k)*2^k. - Philippe Deléham, Feb 25 2012
E.g.f.: exp(2*x)*(cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x)). - Stefano Spezia, May 26 2024
MATHEMATICA
LinearRecurrence[{4, -2}, {1, 6}, 30] (* Harvey P. Dale, Jan 31 2015 *)
PROG
(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] ]; // Klaus Brockhaus, Jul 27 2009
(PARI) x='x+O('x^30); Vec((1+2*x)/(1-4*x+2*x^2)) \\ G. C. Greubel, Jan 27 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Aug 06 2005
EXTENSIONS
Edited by N. J. A. Sloane, Jul 27 2009 using new definition from Al Hakanson (hawkuu(AT)gmail.com)
STATUS
approved