login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A110047 Expansion of (1+2*x-4*x^2)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)). 3
1, 6, 28, 144, 688, 3360, 16192, 78336, 378112, 1826304, 8817664, 42577920, 205582336, 992649216, 4792926208, 23142334464, 111741042688, 539533639680, 2605098729472, 12578530000896, 60734514921472, 293252181786624, 1415946786832384, 6836795882864640 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Note (see program code): ibaseseq[A*B] = A057087, basejseq[A*B] = A099582, tesseq[A*B] = A110046.
LINKS
FORMULA
a(n) = 4*a(n-1) + 8*a(n-2) - 16*a(n-3) - 16*a(n-4). - Matthew House, Feb 17 2017
a(n) = (-3*(2-2*sqrt(2))^n*(-2+sqrt(2)) + 2^n*(-2*(1+(-1)^n)+3*(1+sqrt(2))^n*(2+sqrt(2)))) / 8. - Colin Barker, Feb 17 2017
MAPLE
seriestolist(series((1+2*x-4*x^2)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: -kbasekseq[A*B] with A = + 'i - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = - .5'i + .5'j + 'k - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'
MATHEMATICA
CoefficientList[Series[(1 + 2 x - 4 x^2)/((2 x + 1)(2 x - 1)(4 x^2 + 4 x - 1)), {x, 0, 21}], x] (* or *)
LinearRecurrence[{4, 8, -16, -16}, {1, 6, 28, 144}, 22] (* Michael De Vlieger, Feb 17 2017 *)
PROG
(PARI) Vec((1+2*x-4*x^2) / ((2*x+1)*(2*x-1)*(4*x^2+4*x-1)) + O(x^30)) \\ Colin Barker, Feb 17 2017
CROSSREFS
Sequence in context: A053783 A216383 A283094 * A163029 A309490 A344755
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Jul 10 2005
EXTENSIONS
Definition corrected by Matthew House, Feb 17 2017
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)