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A172123
Number of ways to place 2 nonattacking bishops on an n X n board.
17
0, 4, 26, 92, 240, 520, 994, 1736, 2832, 4380, 6490, 9284, 12896, 17472, 23170, 30160, 38624, 48756, 60762, 74860, 91280, 110264, 132066, 156952, 185200, 217100, 252954, 293076, 337792, 387440, 442370, 502944, 569536, 642532
OFFSET
1,2
REFERENCES
E. Bonsdorff, K. Fabel, O. Riihimaa, Schach und Zahl, 1966, p. 51-63
LINKS
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
Cf. A036464.
Sequence in context: A247194 A102198 A100207 * A298190 A299084 A245457
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 26 2010
STATUS
approved