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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A190401 Number of ways to place 6 nonattacking grasshoppers on a toroidal chessboard of size n x n. 2
0, 0, 0, 384, 19100, 557808, 5841780, 41338400, 209264796, 859752800, 2982181004, 9131392296, 25196132260, 63968987264, 151223202900, 336724832384, 711538908572, 1437022315440, 2787781494732, 5219454908200, 9464698212228 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The Grasshopper moves on the same lines as a queen, but must jump over a hurdle to land on the square immediately beyond.

LINKS

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

V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech)

FORMULA

Explicit formula: a(n) = 1/720*n^2*(n^10 -15n^8 -480n^7 +2245n^6 + 2400n^5 +27255n^4 -342480n^3 +639934n^2 +471600n -865080) + 1/4*n^2*(-1)^n*(8n^4 -40n^3 +17n^2 -272n +1608), n>8.

G.f.: -4x^4*(128x^24 -768x^23 -8x^22 +9258x^21 -17442x^20 -25593x^19 +103542x^18 -19695x^17 -252858x^16 +225766x^15 +297416x^14 -465166x^13 -63474x^12 +488076x^11 +515008x^10 +582376x^9 +2358586x^8 +2976026x^7 +6280504x^6 +4731396x^5 +2785972x^4 +664045x^3 +111570x^2 +4199x +96)/((x-1)^13*(x+1)^7).

MATHEMATICA

CoefficientList[Series[- 4 x^3 (128 x^24 - 768 x^23 - 8 x^22 + 9258 x^21 - 17442 x^20 - 25593 x^19 + 103542 x^18 - 19695 x^17 - 252858 x^16 + 225766 x^15 + 297416 x^14 - 465166 x^13 - 63474 x^12 + 488076 x^11 + 515008 x^10 + 582376 x^9 + 2358586 x^8 + 2976026 x^7 + 6280504 x^6 + 4731396 x^5 + 2785972 x^4 + 664045 x^3 + 111570 x^2 + 4199 x + 96) / ((x - 1)^13 (x + 1)^7), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 03 2013 °)

CROSSREFS

Cf.: A190398, A190399, A190400.

Sequence in context: A281656 A128967 A168675 * A256727 A023098 A188783

Adjacent sequences: A190398 A190399 A190400 * A190402 A190403 A190404

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, May 10 2011

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 December 8 14:17 EST 2022. Contains 358693 sequences. (Running on oeis4.)