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!)
A172201 Number of ways to place 3 nonattacking amazons (superqueens) on an n X n board. 5
0, 0, 0, 0, 48, 424, 1976, 6616, 17852, 41544, 86660, 166288, 298616, 508200, 827168, 1296744, 1968676, 2907016, 4189772, 5910944, 8182400, 11136168, 14926536, 19732600, 25760588, 33246664, 42459476, 53703216, 67320392, 83695144 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
An amazon (superqueen) moves like a queen and a knight.
REFERENCES
Panos Louridas, idee & form 93/2007, pp. 2936-2938.
LINKS
FORMULA
Explicit formula (Panos Louridas, 2007): a(n) = (2*n^6 - 20*n^5 + 31*n^4 + 314*n^3 - 1452*n^2 + 2040*n - 672)/12 if n is even (n >= 4) and a(n) = (2*n^6 - 20*n^5 + 31*n^4 + 314*n^3 - 1452*n^2 + 2034*n - 669)/12 if n is odd (n >= 5).
G.f.: 4*x^5*(12+46*x+60*x^2+32*x^3-23*x^4-13*x^5+7*x^6-x^7)/((1+x)^2*(1-x)^7). - Vaclav Kotesovec, Mar 24 2010
a(n) = (1/24)*(4*n^6 - 40*n^5 + 62*n^4 + 628*n^3 - 2904*n^2 + 4074*n - 1341 + 3*(-1)^n*(2*n-1)) - 20*[n=1] - 8*[n=2] + 4*[n=3]. - G. C. Greubel, Apr 29 2022
MATHEMATICA
CoefficientList[Series[4*x^5*(12+46*x+60*x^2+32*x^3-23*x^4-13*x^5+7*x^6-x^7)/((1+x)^2*(1-x)^7), {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0, 0, 0, 0] cat Coefficients(R!( 4*x^5*(12+46*x+60*x^2+32*x^3-23*x^4-13*x^5+7*x^6-x^7)/((1+x)^2*(1-x)^7 ))); // G. C. Greubel, Apr 29 2022
(SageMath) [(1/24)*(4*n^6 -40*n^5 +62*n^4 +628*n^3 -2904*n^2 +4074*n -1341 +3*(-1)^n*(2*n-1)) -4*(5*bool(n==1) +2*bool(n==2) -bool(n==3)) for n in (1..40)] # G. C. Greubel, Apr 29 2022
CROSSREFS
Sequence in context: A019558 A339761 A232917 * A249293 A347168 A281374
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 29 2010
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 June 20 23:53 EDT 2024. Contains 373535 sequences. (Running on oeis4.)