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A110058 Number of nonnegative integer matrices of order n for which all row and column sums equal n. 4
1, 1, 3, 55, 10147, 22069251, 602351808741, 215717608046511873, 1046591482728407939338275, 70417932475495769964322670258947, 66880713903767740581650957184096513655153, 909176713758393122455793478657031533216492953328933, 178876969166665269546249744608783223036842010760723370462856181, 514016665650183402309555825250370336139392333285719205357202846243695510965 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Computed by a method that involves summing a multivariate generating function over roots of unity.
LINKS
E. R. Canfield, B. D. McKay, Asymptotic enumeration of integer matrices with large equal row and column sums, Combinatorica 30 (6) (2010) 655-680
FORMULA
log a(n) = 2(log 2)*n^2 - n*(log n) - n*(log 4*Pi) + (log n) + O(1). - Igor Pak, May 15 2019
EXAMPLE
a(2) = 3 due to the matrices [1,1 | 1,1], [0,2 | 2,0] and [2,0 | 0,2].
PROG
(Sage)
from sage.combinat.integer_matrices import IntegerMatrices
[IntegerMatrices([n]*n, [n]*n).cardinality() for n in (0..6)] # Freddy Barrera, Dec 27 2018
CROSSREFS
Main diagonal of A257493 and A333901.
Sequence in context: A172932 A172950 A172962 * A083869 A290773 A119188
KEYWORD
nonn
AUTHOR
Brendan McKay, Sep 04 2005
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Apr 26 2015
STATUS
approved

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Last modified April 23 07:16 EDT 2024. Contains 371905 sequences. (Running on oeis4.)