|
|
A259799
|
|
Array read by antidiagonals upwards: T(n,k) = number of partitions of k^n into n-th powers (n>=1, k>=0).
|
|
11
|
|
|
1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 5, 1, 1, 2, 5, 8, 7, 1, 1, 2, 7, 17, 19, 11, 1, 1, 2, 9, 36, 62, 43, 15, 1, 1, 2, 13, 88, 253, 258, 98, 22, 1, 1, 2, 19, 218, 1104, 1886, 1050, 220, 30, 1, 1, 2, 27, 550, 5082, 15772, 14800, 4365, 504, 42, 1, 1, 2, 40, 1413, 24119, 140549, 241582, 118238, 18012, 1116, 56
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
LINKS
|
|
|
EXAMPLE
|
The array begins:
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, ...
1, 1, 2, 4, 8, 19, 43, 98, 220, 504, ...
1, 1, 2, 5, 17, 62, 258, 1050, 4365, 18012, ...
1, 1, 2, 7, 36, 253, 1886, 14800, 118238, ...
1, 1, 2, 9, 88, 1104, 15772, 241582, ...
...
|
|
MAPLE
|
b:= proc(n, i, k) option remember; `if`(n=0 or i=1, 1,
`if`(i=2, 1+iquo(n, i^k), b(n, i-1, k)+
`if`(i^k>n, 0, b(n-i^k, i, k))))
end:
T:= (n, k)-> b(k^n, k, n):
|
|
MATHEMATICA
|
b[n_, i_, k_] := b[n, i, k] = If[n==0 || i==1, 1, If[i==2, 1+Quotient[n, i^k], b[n, i-1, k] + If[i^k>n, 0, b[n-i^k, i, k]]]]; T[n_, k_] := b[k^n, k, n]; Table[ Table[ T[d-k, k], {k, 0, d-1}], {d, 1, 12}] // Flatten (* Jean-François Alcover, Jul 15 2015, after Alois P. Heinz *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|