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!)
A172211 Number of ways to place 6 nonattacking bishops on a 6 X n board. 1
1, 16, 313, 2320, 12160, 53744, 209428, 683524, 1905625, 4664384, 10297579, 20907590, 39664250, 71114916, 121559433, 199459466, 315906248, 485124352, 725031335, 1057839684, 1510706686, 2116429956, 2914190277, 3950340692 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vaclav Kotesovec and Vincenzo Librandi, Table of n, a(n) for n = 1..1000 (first 32 terms from V. Kotesovec).

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

FORMULA

Explicit formula (Vaclav Kotesovec, Jan 28 2010): a(n) = (648n^6-17820n^5+240930n^4-2011545n^3+10806047n^2-35094560n+53430940)/10, n>=25. For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - (2k-1)/2/(k-2)!*(kn)^(k-1) + ...

G.f.: -x*(2*x^30-6*x^29+14*x^28-26*x^27+44*x^26-220*x^25+596*x^24-1060*x^23+1654*x^22

-2266*x^21+5622*x^20-13570*x^19+19848*x^18-22392*x^17+24048*x^16-30525*x^15+57673*x^14

-80154*x^13+61962*x^12-30874*x^11+25832*x^10-9360*x^9+16960*x^8-4710*x^7+18006*x^6+6928*x^5

+1968*x^4+430*x^3+222*x^2+9*x+1)/(x-1)^7. - Vaclav Kotesovec, Mar 25 2010

MATHEMATICA

CoefficientList[Series[-(2 x^30 - 6 x^29 + 14 x^28 - 26 x^27 + 44 x^26 - 220 x^25 + 596 x^24 - 1060 x^23 + 1654 x^22 - 2266 x^21 + 5622 x^20 - 13570 x^19 + 19848 x^18 - 22392 x^17 + 24048 x^16 - 30525 x^15 + 57673 x^14 - 80154 x^13 + 61962 x^12 - 30874 x^11 + 25832 x^10 - 9360 x^9 + 16960 x^8 - 4710 x^7 + 18006 x^6 + 6928 x^5 + 1968 x^4 + 430 x^3 + 222 x^2 + 9 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)

CROSSREFS

Cf. A061992, A172207, A172208, A172210.

Sequence in context: A039746 A232834 A232841 * A254151 A053856 A208266

Adjacent sequences:  A172208 A172209 A172210 * A172212 A172213 A172214

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

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 21:51 EST 2016. Contains 278755 sequences.