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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A172124 Number of ways to place 3 nonattacking bishops on an n X n board. 15
0, 0, 26, 232, 1124, 3896, 10894, 26192, 56296, 110960, 204130, 355000, 589196, 940072, 1450134, 2172576, 3172944, 4530912, 6342186, 8720520, 11799860, 15736600, 20711966, 26934512, 34642744, 44107856, 55636594, 69574232 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

E. Bonsdorff, K. Fabel, O. Riihimaa, Schach und Zahl, 1966, p. 51-63

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

FORMULA

Explicit formulas (Karl Fabel, 1966): a(n) = n(n - 2)(2n^4 - 4n^3 + 7n^2 - 6n + 4)/12 if n is even, and a(n) = (n - 1)(2n^5 - 6n^4 + 9n^3 - 11n^2 + 5n - 3)/12 if n is odd.

G.f.: -2*x^3*(3*x^4+18*x^3+48*x^2+38*x+13)/((x-1)^7*(x+1)). [.Vaclav Kotesovec, Mar 25 2010]

a(n) = (2*(n-2)*n*(2*n^4-4*n^3+7*n^2-6*n+4)-3*(-1)^n+3)/24. [Bruno Berselli, May 26 2013]

MATHEMATICA

CoefficientList[Series[-2 x^2 (3 x^4 + 18 x^3 + 48 x^2 + 38 x + 13) / ((x-1)^7 (x+1)), {x, 0, 30}], x] (* Vincenzo Librandi, May 26 2013 *)

CROSSREFS

Cf. A047659, A172123.

Sequence in context: A159519 A110486 A098994 * A196633 A196638 A163726

Adjacent sequences:  A172121 A172122 A172123 * A172125 A172126 A172127

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 26 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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 8 10:49 EST 2016. Contains 278939 sequences.