login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123071 Bishops on a 2n+1 X 2n+1 board (see Robinson paper for details). 3
1, 2, 4, 12, 36, 120, 400, 1520, 5776, 23712, 97344, 431808, 1915456, 9012608, 42406144, 210988800, 1049760000, 5475340800, 28558296064, 155672726528, 848579961856, 4810614454272, 27271456395264, 160376430784512, 943132599095296, 5735299537018880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). [The sequence S(2k+1).]

FORMULA

Conjecture: 2*a(n) +a(n-1) -2*n*a(n-2) +(-n-10)*a(n-3) -2*(n-2)*(n+2)*a(n-4) +(-n^2-2*n+23)*a(n-5) +2*(n-5)*(n^2-7*n+11)*a(n-6) +(n-6)*(n-5)^2*a(n-7)=0. - R. J. Mathar, Apr 02 2017

MAPLE

For Maple program see A005635.

# alternative

# this is A000898, replicated as 1, 1, 2, 2, 6, 6, 20, 20, 76, 76, ...

B := proc(n)

    if n=0 or n= -2 then

        1 ;

    elif type (n, 'odd') then

        procname(n-1) ;

    else

        2*procname(n-2)+(n-2)*procname(n-4) ;

    end if;

end proc:

A123071 := proc(n)

    B(n)*B(n+1) ;

end proc:

seq(A123071(n), n=0..20) ; # R. J. Mathar, Apr 02 2017

CROSSREFS

Cf. A202828

Sequence in context: A148208 A245798 A241530 * A048116 A148209 A148210

Adjacent sequences:  A123068 A123069 A123070 * A123072 A123073 A123074

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 28 2006

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 14 07:33 EST 2019. Contains 329111 sequences. (Running on oeis4.)