login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002725 Number of incidence matrices: n X (n+1) binary matrices under row and column permutations.
(Formerly M2957 N1195)
6
1, 3, 13, 87, 1053, 28576, 2141733, 508147108, 402135275365, 1073376057490373, 9700385489355970183, 298434346895322960005291, 31479360095907908092817694945, 11474377948948020660089085281068730, 14568098446466140788730090352230460100956 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(0) = 1 by convention.
REFERENCES
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
Andrew Howroyd, Table of n, a(n) for n = 0..50 (terms 0..23 from Alois P. Heinz)
A. Kerber, Experimentelle Mathematik, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 19 (1988), 77-83. [Annotated scanned copy]
B. Misek, On the number of classes of strongly equivalent incidence matrices, (Czech with English summary) Casopis Pest. Mat. 89 1964 211-218.
FORMULA
a(n) = sum_{1*s_1+2*s_2+...=n, 1*t_1+2*t_2+...=n+1} (fix A[s_1, s_2, ...; t_1, t_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...*1^t_1*t_1!*2^t_2*t_2!*...)) where fix A[...] = 2^sum_{i, j>=1} (gcd(i, j)*s_i*t_j). - Sean A. Irvine, Jul 31 2014
EXAMPLE
a(1) = 3: [0,0], [0,1], [1,1].
a(2) = 13:
000 000 000 000 001 001 001 001 001 011 011 011 111
000 001 011 111 001 010 011 110 111 011 101 111 111
MAPLE
b:= proc(n, i) option remember; `if`(n=0, {0}, `if`(i<1, {},
{seq(map(p-> p+j*x^i, b(n-i*j, i-1))[], j=0..n/i)}))
end:
a:= n-> add(add(2^add(add(igcd(i, j)* coeff(s, x, i)*
coeff(t, x, j), j=1..degree(t)), i=1..degree(s))/
mul(i^coeff(s, x, i)*coeff(s, x, i)!, i=1..degree(s))/
mul(i^coeff(t, x, i)*coeff(t, x, i)!, i=1..degree(t)),
t=b(n+1$2)), s=b(n$2)):
seq(a(n), n=0..12); # Alois P. Heinz, Aug 01 2014
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i<1, {}, Flatten @ Table[ Map[ Function[ {p}, p+j*x^i], b[n-i*j, i-1]], {j, 0, n/i}]]];
a[n_] := Sum[Sum[2^Sum[ Sum [ GCD[i, j]*Coefficient[s, x, i]*Coefficient[t, x, j], {j, 1, Exponent[t, x]}], {i, 1, Exponent[s, x]}] / Product[ i^Coefficient[s, x, i]*Coefficient[s, x, i]!, {i, 1, Exponent[s, x]}] / Product[i^Coefficient[t, x, i]*Coefficient[t, x, i]!, {i, 1, Exponent[t, x]}], {t, b[n+1, n+1]}], {s, b[n, n]}];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Feb 25 2015, after Alois P. Heinz *)
PROG
(PARI) a(n) = A(n+1, n) \\ A defined in A028657. - Andrew Howroyd, Mar 01 2023
CROSSREFS
A diagonal of the array A(m,n) described in A028657. - N. J. A. Sloane, Sep 01 2013
Sequence in context: A001831 A196561 A244755 * A324028 A097711 A114477
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Feb 04 2000
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)