|
Search: id:A110221
|
|
|
| A110221 |
|
Triangle read by rows: T(n,k) (0<=k<=floor(n/2)) is the number of Delannoy paths of length n, having k ED's (a Delannoy path of length n is a path from (0,0) to (n,n), consisting of steps E=(1,0), N=(0,1) and D=(1,1)). |
|
+0
1
|
|
| 1, 3, 11, 2, 45, 18, 195, 120, 6, 873, 720, 90, 3989, 4110, 870, 20, 18483, 22806, 6930, 420, 86515, 124264, 49560, 5320, 70, 408105, 668520, 331128, 52920, 1890, 1936881, 3562830, 2111760, 456120, 29610, 252, 9238023, 18850590, 13020480, 3575880
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Row n has 1+floor(n/2) terms. Row sums are the central Delannoy numbers (A001850). Column 0 yields A026375. Sum(k*T(n,k),k=0..floor(n/2))=2*A002695(n).
|
|
REFERENCES
|
R. A. Sulanke, Objects counted by the central Delannoy numbers, J. of Integer Sequences, 6, 2003, Article 03.1.5.
|
|
FORMULA
|
G.f.=1/(1-z-2tz^2*R-2zR+2z^2*R), where R=[1-z-sqrt(1-6z+5z^2-4tz^2)]/[2z(1-z+tz)].
|
|
EXAMPLE
|
T(2,1)=2 because we have NED and EDN.
Triangle begins:
1;
3;
11,2;
45,18;
195,120,6;
|
|
MAPLE
|
R:=(1-z-sqrt(1-6*z+5*z^2-4*z^2*t))/2/z/(1-z+t*z): G:=1/(1-z-2*t*z^2*R-2*z*R+2*z^2*R): Gser:=simplify(series(G, z=0, 15)): P[0]:=1: for n from 1 to 12 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 12 do seq(coeff(t*P[n], t^k), k=1..1+floor(n/2)) od; # yields sequence in triangular form
|
|
CROSSREFS
|
Cf. A001850, A026375, A002695.
Sequence in context: A096663 A133369 A110123 this_sequence A084466 A084462 A156320
Adjacent sequences: A110218 A110219 A110220 this_sequence A110222 A110223 A110224
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 20 2005
|
|
|
Search completed in 0.002 seconds
|
