|
| |
|
|
A035287
|
|
Number of ways to place a non-attacking white and black rook on n X n chessboard.
|
|
8
| |
|
|
0, 4, 36, 144, 400, 900, 1764, 3136, 5184, 8100, 12100, 17424, 24336, 33124, 44100, 57600, 73984, 93636, 116964, 144400, 176400, 213444, 256036, 304704, 360000, 422500, 492804, 571536, 659344, 756900, 864900, 984064, 1115136, 1258884
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| a(n) is equal to the number of functions f:{1,2,3,4}->{1,2,...,n} such that for fixed different x_1, x_2 in {1,2,3,4} and fixed y_1, y_2 in {1,2,...,n} we have f(x_1)<>y_1 and f(x_2)<>y_2. - Milan R. Janjic (agnus(AT)blic.net), Apr 17 2007
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 21 2009: (Start)
The third differences of certain values of the hypergeometric function 3F2 lead to this sequence i.e. 3F2([1,n+1,n+1], [n+2,n+2], z=1) - 3*3F2([1,n+2,n+2], [n+3,n+3], z=1) + 3*3F2([1,n+3,n+3], [n+4,n+4], z=1) - 3F2([1,n+4,n+4], [n+5,n+5], z=1) = (1/((n+2)*(n+3)))^2 with n = -1, 0, 1,2, .. . See also A162990.
(End)
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Wolfram Research, Hypergeometric Function 3F2, The Wolfram Functions site. [From Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 21 2009]
|
|
|
FORMULA
| a(n) = n^2 * (n-1)^2
a(n) = A002378(n)^2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 11 2006
Contribution from Stephen Crowley (crow(AT)crowlogic.net), Jul 19 2009: (Start)
a(n)=limit(n!*(2*n+1)/(diff(1+polylog(2,x)-polylog(2,x)/x, x$n),x=0) and int(1+polylog(2,x)-polylog(2,x)/x,x=0..1)=Zeta(2)-Zeta(3)
sum((n^2*(n-1)^2)^(-1),n=2..infinity)=2*Zeta(2)-3 (End)
a(n) = 4*A000537(n-1) = 2*A163102(n-1). - Omar E. Pol, Nov 29 2011
|
|
|
MATHEMATICA
| lst={}; Do[s0 = n^2; s1 = (n + 1)^2; AppendTo[lst, s1 * s0], {n, 0, 6!}]; lst (* From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 19 2009 *)
Table[(n - 1)^2 n^2, {n, 30}] (* From Alonso del Arte, May 20 2011 *)
|
|
|
PROG
| (Sage): [n^2*(n-1)^2 for n in xrange(1, 35)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 03 2009]
(MAGMA) [n^2 * (n-1)^2: n in [1..40]]; // Vincenzo Librandi, May 21 2011
|
|
|
CROSSREFS
| Cf. A002378.
Sequence in context: A060783 A125756 A173961 * A176471 A183354 A204504
Adjacent sequences: A035284 A035285 A035286 * A035288 A035289 A035290
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Erich Friedman (erich.friedman(AT)stetson.edu)
|
| |
|
|
