

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 upright.


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(m1,n)+2*a(m,n1)a(m1,n1)3*a(m2,n1)3*a(m1,n2)+4*a(m2,n2), where m >=3 or n >= 3 and a(m,n)=0 if m <= 0 or n <= 0; generating function = (xyx^2yxy^2+x^3y^2+x^2y^3x^3y^3)/(12x2y+xy+3x^2y+3xy^24x^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



