A182563 Number of ways to place n non-attacking semi-knights on an n x n chessboard.

1, 6, 70, 1289, 33864, 1148760, 47700972, 2344465830, 133055587660, 8559364525414, 615266768106190, 48861588247978827, 4247584874013608724, 401107335066453376830, 40880928693752664368224, 4472281486633326131737868, 522658199001494278018633508

Offset

1,2

Comments

Semi-knight is a semi-leaper [1,2]. Moves of a semi-knight are allowed only in [2,1] and [-2,-1]. See also semi-bishops (A187235).

Links

Christian Sievers, Table of n, a(n) for n = 1..338

V. Kotesovec, Non-attacking chess pieces, 6ed, p.289

Formula

Asymptotic: a(n) ~ n^(2n)/n!*exp(-3/2).

Prog

(PARI) f(n)=polcoef(prod(i=1, n, prod(j=1, if(i<=2, n, 1), my(m=min((n+2-i)\2, n+1-j)); sum(k=0, (m+1)\2, binomial(m+1-k, k)*x^k)+O(x*x^n))), n) \\ Christian Sievers, Dec 09 2025

Crossrefs

Cf. A182562, A201540, A201513, A002465, A201511, A197989, A201861.

Sequence in context: A392206 A394492 A365057 * A211036 A284215 A050788

Adjacent sequences: A182560 A182561 A182562 * A182564 A182565 A182566

Keyword

nonn

Author

Vaclav Kotesovec, May 05 2012

Extensions

a(16) from Vaclav Kotesovec, May 24 2021

a(17) from Christian Sievers, Dec 09 2025

Status

approved