|
|
A319453
|
|
Number T(n,k) of partitions of n into exactly k nonzero decimal palindromes; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
|
|
14
|
|
|
1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 3, 3, 2, 1, 1, 0, 1, 3, 4, 3, 2, 1, 1, 0, 1, 4, 5, 5, 3, 2, 1, 1, 0, 1, 4, 7, 6, 5, 3, 2, 1, 1, 0, 0, 5, 8, 9, 7, 5, 3, 2, 1, 1, 0, 1, 4, 10, 11, 10, 7, 5, 3, 2, 1, 1, 0, 0, 5, 11, 15, 13, 11, 7, 5, 3, 2, 1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,13
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = [x^n y^k] 1/Product_{j>=2} (1-y*x^A002113(j)).
|
|
EXAMPLE
|
Triangle T(n,k) begins:
1;
0, 1;
0, 1, 1;
0, 1, 1, 1;
0, 1, 2, 1, 1;
0, 1, 2, 2, 1, 1;
0, 1, 3, 3, 2, 1, 1;
0, 1, 3, 4, 3, 2, 1, 1;
0, 1, 4, 5, 5, 3, 2, 1, 1;
0, 1, 4, 7, 6, 5, 3, 2, 1, 1;
0, 0, 5, 8, 9, 7, 5, 3, 2, 1, 1;
0, 1, 4, 10, 11, 10, 7, 5, 3, 2, 1, 1;
0, 0, 5, 11, 15, 13, 11, 7, 5, 3, 2, 1, 1;
...
|
|
MAPLE
|
p:= proc(n) option remember; local i, s; s:= ""||n;
for i to iquo(length(s), 2) do if
s[i]<>s[-i] then return false fi od; true
end:
h:= proc(n) option remember; `if`(n<1, 0,
`if`(p(n), n, h(n-1)))
end:
b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,
b(n, h(i-1))+expand(x*b(n-i, h(min(n-i, i)))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n, h(n))):
seq(T(n), n=0..14);
|
|
CROSSREFS
|
Columns k=0-10 give: A000007, A136522 (for n>0), A319468, A261131, A319469, A319470, A319471, A319472, A319473, A319474, A319475.
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|