OFFSET
1,2
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
Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = n*(n - 1)*(3*n^2 - n + 2)/6.
G.f.: -2*x^2*(x+1)*(x+2)/(x-1)^5. - Vaclav Kotesovec, Mar 25 2010
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Vincenzo Librandi, Apr 29 2013
MATHEMATICA
CoefficientList[Series[-2 x (x+1)(x+2)/(x-1)^5, {x, 0, 80}], x] (* Vincenzo Librandi, Apr 29 2013 *)
PROG
(Magma) [n*(n-1)*(3*n^2-n+2)/6: n in [1..40]]; /* or */ I:=[0, 4, 26, 92, 240]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, Apr 29 2013
(PARI) a(n)=n*(n-1)*(3*n^2-n+2)/6 \\ Charles R Greathouse IV, Jun 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 26 2010
STATUS
approved