login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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.

LINKS

Alois P. Heinz, Rows n = 1..45, flattened

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).

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

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1}, If[i<1, {}, Join[b[n, i-1, k], Table[ Function[#*i!^j] /@ b[n-i*j, i-1, k-j], {j, 1, Min[n/i, k]}] // Flatten] // Union] ]; T[n_, k_] := Length[b[n, n, k]]; Table[Table[T[n, k], {k, 1, n}], {n, 1, 10}] // Flatten (* Jean-Fran├žois Alcover, Mar 12 2015, after Alois P. Heinz *)

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 03:32 EST 2016. Contains 278837 sequences.