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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A113066 Expansion of (1+x)^2/((x^2+x+1)*(x^2+3*x+1)). 0
1, -2, 4, -10, 27, -72, 189, -494, 1292, -3382, 8855, -23184, 60697, -158906, 416020, -1089154, 2851443, -7465176, 19544085, -51167078, 133957148, -350704366, 918155951, -2403763488, 6293134513, -16475640050, 43133785636, -112925716858, 295643364939, -774004377960 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform gives signed version of A093040. a(n) + a(n+1) = ((-1)^(n+1))A109961(n+1). a(n) + a(n+1) + a(n+2) = ((-1)^n)A001906(n+2) = ((-1)^n)F(2n+4)

The positive sequence has g.f. (1-x)^2/((1-x+x^2)(1-3x+x^2)) and a(n)=sum{k=0..n, C(n+k+1,n-k)*(1+(-1)^k)/2}. [From Paul Barry, Jul 06 2009]

REFERENCES

C. Dement, Floretion Integer Sequences (work in progress).

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (-4,-5,-4,-1).

FORMULA

a(n) = A049347(n)/2 +(-1)^n*A001906(n+1)/2. [From R. J. Mathar, Nov 10 2009]

PROG

Floretion Algebra Multiplication Program, FAMP Code: 2basei[C*F]; C = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki'; F = + .5'i + .5'ii' + .5'ij' + .5'ik'

CROSSREFS

Cf. A113067, A113068, A093040, A109961, A001906.

Sequence in context: A173758 A272603 A272602 * A002459 A216434 A220829

Adjacent sequences:  A113063 A113064 A113065 * A113067 A113068 A113069

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Oct 13 2005

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 20 10:41 EST 2017. Contains 294963 sequences.