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A002728 Number of n X (n+2) binary matrices.
(Formerly M3593 N1457)
4
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

Alois P. Heinz, Table of n, a(n) for n = 0..23

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 *)

CROSSREFS

Cf. A002623, A002727, A006148, A002724, A002725.

A diagonal of the array A(m,n) described in A028657. - N. J. A. Sloane, Sep 01 2013

Sequence in context: A112370 A197961 A203120 * A062494 A183274 A303330

Adjacent sequences:  A002725 A002726 A002727 * A002729 A002730 A002731

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vladeta Jovovic, Feb 04 2000

STATUS

approved

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Last modified January 22 12:13 EST 2019. Contains 319363 sequences. (Running on oeis4.)