OFFSET
1,4
COMMENTS
Wazir is a (fairy chess) leaper [0,1].
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Grid Graph
Wikipedia, Fairy chess piece
Wikipedia, Wazir (chess)
FORMULA
a(n) = (n^10-50n^8+40n^7+995n^6-1560n^5-8890n^4+21080n^3+24264n^2-97440n+59520)/120, n>=4.
For any fixed value of k > 1, a(n) = n^(2k)/k! - 5/2/(k-2)!*n^(2k-2) + ...
G.f.: x^3 * (6*x^11 -26*x^10 -93*x^9 +527*x^8 +490*x^7 -6710*x^6 +13630*x^5 -3954*x^4 -26364*x^3 -7452*x^2 -293*x -1) / (x-1)^11. - Vaclav Kotesovec, Apr 29 2011
a(n) = A232833(n,5). - R. J. Mathar, Apr 11 2024
MATHEMATICA
CoefficientList[Series[x^2 (6 x^11 - 26 x^10 - 93 x^9 + 527 x^8 + 490 x^7 - 6710 x^6 + 13630 x^5 - 3954 x^4 - 26364 x^3 - 7452 x^2 - 293 x - 1) / (x - 1)^11, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 29 2010
EXTENSIONS
Corrected a(4) and g.f., Vaclav Kotesovec, Apr 29 2011.
More terms from Vincenzo Librandi, May 28 2013
STATUS
approved