|
| |
|
|
A213008
|
|
Triangle of number of distinct values of multinomial coefficients corresponding to sequence A026820.
|
|
2
|
|
|
|
1, 1, 2, 1, 2, 3, 1, 3, 4, 5, 1, 3, 5, 6, 7, 1, 4, 7, 9, 10, 11, 1, 4, 8, 10, 12, 13, 14, 1, 5, 9, 14, 16, 18, 19, 20, 1, 5, 12, 17, 21, 23, 25, 26, 27, 1, 6, 13, 21, 26, 30, 32, 34, 35, 36, 1, 6, 16, 25, 33, 37, 41, 43, 45, 46, 47, 1, 7, 19, 32, 42, 50, 54, 58, 60, 62, 63, 64
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
Differs from A026820 after position 24.
Includes sequence A070289 when k=n.
|
|
|
REFERENCES
|
Katsuhisa Yamanaka, Shin-ichiro Kawano, Yosuke Kikuchi, Shin-ichi Nakano, Constant Time Generation of Integer Partitions, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.E90-A, no.5, pp.888-895, (May-2007)
|
|
|
LINKS
|
Alois P. Heinz, Rows n = 1..45, flattened
Sergei Viznyuk, C-Program, same, local copy.
|
|
|
EXAMPLE
|
Triangle begins:
1;
1, 2;
1, 2, 3;
1, 3, 4, 5;
1, 3, 5, 6, 7;
1, 4, 7, 9, 10, 11;
1, 4, 8, 10, 12, 13, 14;
Thus, for n=7 and k=6 there are 13 distinct values of multinomial coefficients corresponding to partitions of n=7 into at most k=6 parts. The corresponding number of partitions from sequence A026820 is 14. That is because partitions 7=4+1+1+1 and 7=3+2+2 produce the same value of multinomial coefficient 7!/(4!*1!*1!*1!)=7!/(3!*2!*2!).
|
|
|
MAPLE
|
b:= proc(n, i, k) option remember; if n=0 then {1} elif i<1
then {} else {b(n, i-1, k)[], seq(map(x-> x*i!^j,
b(n-i*j, i-1, k-j))[], j=1..min(n/i, k))} fi
end:
T:= (n, k)-> nops(b(n, n, k)):
seq (lprint(seq(T(n, k), k=1..n)), n=1..10); # Alois P. Heinz, Aug 14 2012
|
|
|
CROSSREFS
|
Cf. A026820, A070289.
Sequence in context: A066010 A209556 A109974 * A215520 A026820 A091438
Adjacent sequences: A213005 A213006 A213007 * A213009 A213010 A213011
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Sergei Viznyuk, Jun 01 2012
|
|
|
STATUS
|
approved
|
| |
|
|
