|
Search: id:A143453
|
|
|
| A143453 |
|
Square array A(n,k) of numbers of length n ternary words with at least k 0-digits between any other digits (n,k >= 0), read by antidiagonals. |
|
+0
7
|
|
| 1, 1, 3, 1, 3, 9, 1, 3, 5, 27, 1, 3, 5, 11, 81, 1, 3, 5, 7, 21, 243, 1, 3, 5, 7, 13, 43, 729, 1, 3, 5, 7, 9, 23, 85, 2187, 1, 3, 5, 7, 9, 15, 37, 171, 6561, 1, 3, 5, 7, 9, 11, 25, 63, 341, 19683, 1, 3, 5, 7, 9, 11, 17, 39, 109, 683, 59049, 1, 3, 5, 7, 9, 11, 13, 27, 57, 183, 1365, 177147
(list; table; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
FORMULA
|
G.f. of column k: 1/(x^k*(1-x-2*x^(k+1))). A(n,k) = 3^n if k=0, else A(n,k) = 2*n+1 if n<=k+1, else A(n,k) = A(n-1,k) + 2*A(n-k-1,k).
|
|
EXAMPLE
|
A (3,1) = 11, because 11 ternary words of length 3 have at least 1 0-digit between any other digits: 000, 001, 002, 010, 020, 100, 101, 102, 200, 201, 202.
Square array A(n,k) begins:
1 1 1 1 1 1 1 1 ...
3 3 3 3 3 3 3 3 ...
9 5 5 5 5 5 5 5 ...
27 11 7 7 7 7 7 7 ...
81 21 13 9 9 9 9 9 ...
243 43 23 15 11 11 11 11 ...
729 85 37 25 17 13 13 13 ...
2187 171 63 39 27 19 15 15 ...
|
|
MAPLE
|
A := proc (n::nonnegint, k::nonnegint) option remember; if k=0 then 3^n elif n<=k+1 then 2*n+1 else A(n-1, k) +2*A(n-k-1, k) fi end: seq (seq (A(n, d-n), n=0..d), d=0..14);
|
|
CROSSREFS
|
Column k=0: A000244, k=1: A001045(n+2), k=2: A003229(n+1) and A077949(n+2), k=3: A052942(n+3), k=4: A143447, k=5: A143448, k=6: A143449, k=7: A143450, k=8: A143451, k=9: A143452. Diagonal: A005408.
Sequence in context: A087000 A010282 A119265 this_sequence A164308 A082511 A088442
Adjacent sequences: A143450 A143451 A143452 this_sequence A143454 A143455 A143456
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 16 2008
|
|
|
Search completed in 0.004 seconds
|
