

A000412


Number of bipartite partitions of n white objects and 3 black ones.
(Formerly M2657 N1060)


4



3, 7, 16, 31, 57, 97, 162, 257, 401, 608, 907, 1325, 1914, 2719, 3824, 5313, 7316, 9973, 13495, 18105, 24132, 31938, 42021, 54948, 71484, 92492, 119120, 152686, 194887, 247693, 313613, 395547, 497154, 622688, 777424, 967525, 1200572, 1485393, 1832779, 2255317
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

Number of ways to factor p^n*q^3 where p and q are distinct primes.
a(n) = if n <= 3 then A054225(3,n) else A054225(n,3). [Reinhard Zumkeller, Nov 30 2011]


REFERENCES

F. C. Auluck, On partitions of bipartite numbers. Proc. Cambridge Philos. Soc. 49, (1953). 7283.
M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956, p. 1.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100
F C Auluck, On ptns of bipartite numbers, annotated scan of a few pages.
M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956 (Annotated scanned pages from, plus a review)


MATHEMATICA

max = 40; col = 3; s1 = Series[Product[1/(1x^(nk)*y^k), {n, 1, max+2}, {k, 0, n}], {y, 0, col}] // Normal; s2 = Series[s1, {x, 0, max+1}]; a[n_] := SeriesCoefficient[s2, {x, 0, n}, {y, 0, col}]; Table[ a[n] , {n, 0, max}] (* JeanFrançois Alcover, Mar 13 2014 *)


CROSSREFS

Column 3 of A054225.
Cf. A005380.
Sequence in context: A184677 A224340 A240739 * A192964 A179904 A161810
Adjacent sequences: A000409 A000410 A000411 * A000413 A000414 A000415


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Edited by Christian G. Bower, Jan 08 2004


STATUS

approved



