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
Vaclav Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = (n^8 - 54*n^6 + 144*n^5 + 1019*n^4 - 5232*n^3 - 2022*n^2 + 51120*n - 77184)/24, n >= 6. (Karl Fabel, 1966)
G.f.: x^2 * ( 1 + 9*x + 286*x^2 + 1292*x^3 - 345*x^4 +3099*x^5 - 5142*x^6 + 3606*x^7 - 1162*x^8 - 390*x^9 + 690*x^10 - 312*x^11 + 48*x^12) / (1-x)^9. - Vaclav Kotesovec, Mar 25 2010
E.g.f.: x^2/2! + 18*x^3/3! + 412*x^4/4! + 4436*x^5/5! + (1/120)*(385920 + 161040*x + 17940*x^2 - 1200*x^3 - 2660*x^4 - 4484*x^5 + (-385920 + 224880*x - 49860*x^2 + 2940*x^3 + 3250*x^4 + 1920*x^5 + 1060*x^6 + 140*x^7 + 5*x^8)*exp(x)). - G. C. Greubel, Apr 19 2022
MATHEMATICA
CoefficientList[Series[x*(1 +9*x +286*x^2 +1292*x^3 -345*x^4 +3099*x^5 -5142*x^6 +3606*x^7 -1162*x^8 -390*x^9 +690*x^10 -312*x^11 +48*x^12)/(1-x)^9, {x, 0, 40}], x] (* Vincenzo Librandi, May 26 2013 *)
PROG
(Magma) [0, 1, 18, 412, 4436] cat [(n^8 -54*n^6 +144*n^5 +1019*n^4 -5232*n^3 -2022*n^2 +51120*n -77184)/24: n in [6..50]]; // G. C. Greubel, Apr 19 2022
(SageMath) [0, 1, 18, 412, 4436] + [(n^8 -54*n^6 +144*n^5 +1019*n^4 -5232*n^3 -2022*n^2 +51120*n -77184)/24 for n in (6..50)] # G. C. Greubel, Apr 19 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 26 2010
STATUS
approved