login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187235 Number of ways to place n nonattacking semi-bishops on an n X n board. 20
1, 5, 51, 769, 15345, 381065, 11323991, 391861841, 15476988033, 687029386845, 33861652925595, 1834814222811361, 108411291759763681, 6936921762461326545, 477881176664541171375, 35264213540563039871265, 2775185864375851234241985, 232010235620834821000259765, 20534530616200868936398461635 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Two semi-bishops do not attack each other if they are in the same NorthWest-SouthEast diagonal.

Conjecture: Number of parity preserving permutations of the set {1, 2, ..., 2n+1} with exactly n+1 cycles (see A246117). - Peter Luschny, Feb 09 2015

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..350

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 260-265.

FORMULA

a(n)/(n-1)! ~ 0.24252191 * 4.9108149^n where the second constant is 1/(z*(1-z)) = 4.910814964..., where z=0.715331862959... is a root of the equation z=2*(z-1)*log(1-z).

For constants see A238261 and A238262. - Vaclav Kotesovec, Feb 21 2014

a(n) = (-1)^n * Sum_{i=0..n} Stirling1(n,i) * Stirling1(n+1,n-i+1). - Ryan Brooks, May 09 2020

MATHEMATICA

Table[If[n==1, 1, Coefficient[Expand[Product[x+i, {i, 1, n}]*Product[x+i, {i, 1, n-1}], x], x, n-1]], {n, 1, 50}]

Table[(-1)^n*Sum[StirlingS1[n+1, j]*StirlingS1[n, n-j+1], {j, 1, n}], {n, 1, 50}] (* Explicit formula, Vaclav Kotesovec, Mar 24 2011 *)

PROG

(PARI) a(n) = {(-1)^n*sum(i=0, n, stirling(n, i, 1) * stirling(n+1, n-i+1, 1))} \\ Andrew Howroyd, May 09 2020

CROSSREFS

Cf. A238261, A238262, A002465, A099152, A000255, A129256.

Sequence in context: A154886 A268138 A145162 * A318192 A299435 A095839

Adjacent sequences:  A187232 A187233 A187234 * A187236 A187237 A187238

KEYWORD

nonn,nice

AUTHOR

Vaclav Kotesovec, Mar 08 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 25 11:32 EST 2020. Contains 338623 sequences. (Running on oeis4.)