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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132439 Square array a(m,n) read by antidiagonals, where a(m,n) is the number of ways to move a chess queen from the lower left corner to square (m,n), with the queen moving only up, right, or diagonally up-right. 1
1, 1, 1, 2, 3, 2, 4, 7, 7, 4, 8, 17, 22, 17, 8, 16, 40, 60, 60, 40, 16, 32, 92, 158, 188, 158, 92, 32, 64, 208, 401, 543, 543, 401, 208, 64, 128, 464, 990, 1498, 1712, 1498, 990, 464, 128, 256, 1024, 2392, 3985, 5079, 5079, 3985, 2392, 1024, 256 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(m,n) is the sum of all the entries above it plus the sum of all the entries to the left of it plus the sum of all the entries on the northwest diagonal from it.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(1,1)=1;a(1,2)=1;a(1,3)=2;a(2,1)=1;a(2,2)=3;a(2,3)=7;a(3,1)=2;a(3,2)=7;a(3,3)=22;a(m,n) = 2*a(m-1,n)+2*a(m,n-1)-a(m-1,n-1)-3*a(m-2,n-1)-3*a(m-1,n-2)+4*a(m-2,n-2), where m >=3 or n >= 3 and a(m,n)=0 if m <= 0 or n <= 0; generating function = (xy-x^2y-xy^2+x^3y^2+x^2y^3-x^3y^3)/(1-2x-2y+xy+3x^2y+3xy^2-4x^2y^2).

EXAMPLE

The table begins

1 1 2 4 8 16 32 ...

1 3 7 17 40 92 208 ...

2 7 22 60 158 401 990 ...

4 17 60 188 543 1498 3985 ...

8 40 158 543 1712 5079 14430 ...

a(3,4)=4+17+2+7+22+1+7=60

CROSSREFS

Cf. A035002.

Sequence in context: A229012 A207606 A303845 * A116217 A274486 A227961

Adjacent sequences:  A132436 A132437 A132438 * A132440 A132441 A132442

KEYWORD

easy,nonn,tabl

AUTHOR

Martin J. Erickson (erickson(AT)truman.edu), Nov 13 2007

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 January 22 19:47 EST 2020. Contains 331153 sequences. (Running on oeis4.)