login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085293 Product of Lucas (A000204) and a Pell Companion series (A002203). 1
2, 18, 56, 238, 902, 3564, 13862, 54238, 211736, 827298, 3231362, 12623044, 49308482, 192613698, 752401496, 2939092798, 11480914982, 44847668844, 175187526662, 684331472398, 2673190054136, 10442227799538, 40790261396162, 159338166024964, 622419427368002 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Convergent a(n+1)/a(n) = [(1+sqrt5)/2]*(1+sqrt2) = (1.618...)*(2.414213...) = 3.9062796...= (1 + sqrt2 + sqrt5 + sqrt10)/2; (since with large n, A000204 is approximated by PHI^n & A002203 is approximated by (1+sqrt2)^n, with the fractional part of each becoming negligible as n approaches infinity. Check: a(11)/a(10) = 3231362/827298 = 3.9059226...

LINKS

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (2,7,2,-1).

FORMULA

a(n) = A000204(n) * A002203(n), n>0.

a(n) = 2*A085292(n).

a(n) = (((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n) * ((1+sqrt(2))^n + (1-sqrt(2))^n).

a(n) = 2*a(n-1)+7*a(n-2)+2*a(n-3)-a(n-4). G.f.: -2*x*(2*x^3-3*x^2-7*x-1) / (x^4-2*x^3-7*x^2-2*x+1). - Colin Barker, Oct 15 2013

CROSSREFS

Cf. A085292, A000204, A002203.

Sequence in context: A058653 A058794 A114109 * A119118 A213820 A078837

Adjacent sequences:  A085290 A085291 A085292 * A085294 A085295 A085296

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jun 24 2003

EXTENSIONS

More terms from David Wasserman, Jan 31 2005

More terms from Colin Barker, Oct 16 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)