|
|
A060897
|
|
Number of walks of length n on square lattice, starting at origin, staying in first and third quadrants.
|
|
6
|
|
|
1, 4, 12, 44, 144, 528, 1808, 6676, 23536, 87568, 315136, 1180680, 4314560, 16263896, 60138816, 227899484, 850600944, 3238194560, 12177384544, 46542879384, 176110444736, 675431779856, 2568878867200, 9882068082112, 37747540858240, 145593279888736, 558190182662144
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Is there a formula analogous to the (conjectured) formula for A060900?
Could be broken into the number of walks that are constrained to a quadrant and the number that cross the origin. (I.e., 2*A005566(n) + 2*A005566(n-2)*A005568(1) + 2*A005566(n-4)*A005568(2) + ... + All terms that cross the origin twice + three times + ... + Cross floor(n/2) times.) - Benjamin Phillabaum, Mar 13 2011
|
|
LINKS
|
|
|
FORMULA
|
|
|
PROG
|
B(n)={sum(n=0, n, x^n*binomial(n, n\2)*binomial(n+1, (n+1)\2), O(x*x^n))}
C(n)={sum(n=0, (n+1)\2, x^(2*n)*binomial(2*n, n)*binomial(2*n+2, n+1)/((n+1)*(n+2)), O(x*x^n))}
seq(n) = {Vec( 1 + 2*(B(n)-1)/(2-C(n)) )} \\ Andrew Howroyd, Jan 05 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|