Stephen Penrice - cp's OEIS frontend

User: Stephen Penrice

Stephen Penrice has authored 2 sequences.

A248744 Number of different ways one can attack all squares on an n X n chessboard with n rooks.

1, 1, 6, 48, 488, 6130, 92592, 1642046, 33514112, 774478098, 19996371200, 570583424422, 17831721894912, 605743986163706, 22223926472824832, 875786473087350750, 36893467224629215232, 1654480168085245432354, 78692809748219369422848, 3956839189675526769415958

Offset: 0

Stephen Penrice, Apr 09 2017

nonn

Number of minimum (and minimal) dominating sets in the n X n rook graph. - Eric W. Weisstein, Jun 20 2017 and Aug 02 2017

A. M. Yaglom and I. M. Yaglom, Challenging Mathematical Problems with Elementary Solutions, Vol. 1: Combinatorial Analysis and Probability Theory, Dover Publications, 1987, p. 77

Eric Weisstein's World of Mathematics, Minimal Dominating Set
Eric Weisstein's World of Mathematics, Minimum Dominating Set
Eric Weisstein's World of Mathematics, Rook Graph

Main diagonal of A290632 and of A368831.

Cf. A000142, A000312.

A248744:=n->2*n^n-n!: seq(A248744(n), n=0..25); # Wesley Ivan Hurt, Nov 30 2017

Mathematica
```
Table[2 n^n - n!, {n, 20}]
```

a(n) = 2*n^n - n!.

A000511 Number of n-step spiral self-avoiding walks on hexagonal lattice, where at each step one may continue in same direction or make turn of 2*Pi/3 counterclockwise.

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 11, 17, 25, 33, 47, 67, 87, 117, 160, 207, 270, 356, 455, 584, 751, 945, 1195, 1513, 1882, 2345, 2927, 3608, 4446, 5483, 6701, 8180, 9986, 12109, 14664, 17750, 21371, 25694, 30872, 36937, 44127, 52672, 62658, 74429, 88327, 104524, 123518, 145819, 171737, 201990, 237332, 278289, 325901, 381278, 445272, 519381, 605230, 704170, 818357, 950150, 1101634, 1275907, 1476384, 1706226, 1969869, 2272224, 2618007, 3013559, 3465917, 3982025, 4570898, 5242569, 6007170, 6877474, 7867709, 8992510, 10269905, 11719991, 13363733, 15226469, 17336450, 19723485, 22423058, 25474712, 28920541, 32810028, 37198284, 42144403, 47717124, 53992936, 61054313, 68996364, 77924848, 87954283, 99215750, 111854888

Offset: 0

Stephen Penrice (penrice(AT)dimacs.rutgers.edu)

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

J. H. Bruinier, Infinite products in number theory and geometry, arXiv:math/0404427 [math.NT], 2004.
G. S. Joyce and R. Bak, An exact solution for a spiral self-avoiding walk model on the triangular lattice, J. Phys. A: Math. Gen. 18 (1985) L293-L298, esp. p. L297.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

More terms from Sean A. Irvine, Nov 14 2010

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User: Stephen Penrice

A248744 Number of different ways one can attack all squares on an n X n chessboard with n rooks.

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