

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
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OFFSET

1,3


COMMENTS

Differs from A026820 after position 24.
Includes sequence A070289 when k=n.


REFERENCES

Katsuhisa Yamanaka, Shinichiro Kawano, Yosuke Kikuchi, Shinichi Nakano, Constant Time Generation of Integer Partitions, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.E90A, no.5, pp.888895, (May2007)


LINKS

Alois P. Heinz, Rows n = 1..45, flattened
Sergei Viznyuk, CProgram, 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, i1, k)[], seq(map(x> x*i!^j,
b(ni*j, i1, kj))[], 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



