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A002728 Number of n X (n+2) binary matrices.
(Formerly M3593 N1457)
5
1, 4, 22, 190, 3250, 136758, 17256831, 7216495370, 10271202313659, 49856692830176512, 826297617412284162618, 46948445432190686211183650, 9200267975562856184153936960940, 6261904454889790650636380541051266410, 14910331834338546882501064075429145637985605 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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+2} (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
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+2$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, {}, Table[Function[{p}, p + j*x^i]@ b[n-i*j, i-1] , {j, 0, n/i}]]] // Flatten; 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+2, n+2]}], {s, b[n, n]}]; Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Nov 28 2014, after Alois P. Heinz *)
PROG
(PARI) a(n) = A(n+2, 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: A112370 A197961 A203120 * A364624 A062494 A183274
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Feb 04 2000
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)