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A084485 Number of 3 X n 0-1 matrices which have n+2 1's and have no zero rows or zero columns. 1
1, 12, 90, 522, 2595, 11673, 49014, 195828, 753813, 2819475, 10308144, 36998118, 130786695, 456452493, 1575799290, 5389290792, 18281487081, 61569776727, 206040460212, 685584843450, 2269566343611, 7478425876977, 24538396875870, 80206515476892, 261239771497725 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is the number of spanning subgraphs of the complete bipartite graph K(3,n) with n + 2 edges and no isolated vertices. If the subgraphs are also connected then they are spanning trees. The number of spanning trees in K(m,n) is known. See A001787.

LINKS

Table of n, a(n) for n=1..25.

M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013

M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5

Index entries for linear recurrences with constant coefficients, signature (15,-93,305,-558,540,-216)

FORMULA

a(n) = n*(4*(3*n-1)*3^n-9*(n-1)*2^n)/24. - Vladeta Jovovic, May 28 2003

G.f.: x*(1-3*x+3*x^2-17*x^3+33*x^4)/((3*x-1)^3*(2*x-1)^3). - Alois P. Heinz, Sep 24 2012

MAPLE

with(LinearAlgebra): num1s:= (M, m, n)->add(ListTools[Flatten](convert(M, listlist))[j], j=1..m*n): binrows:= n->[seq(convert(i+2^n, base, 2)[1..n], i=1..2^n-1)]: a:= proc(n) local A, L, i, j, k, S, M: S := 0: L := binrows(n): for i from 1 to 2^n-1 do for j from 1 to 2^n-1 do for k from 1 to 2^n-1 do A := Matrix([L[i], L[j], L[k]]); if num1s(A, 3, n)=n+2 and (not has(Matrix([1, 1, 1]).A, 0)) then S := S+1; end if; od; od; od; S; end proc: seq (a(n), n=1..5);

MATHEMATICA

a[n_] := n*(4*(3*n - 1)*3^n - 9*(n - 1)*2^n)/24;

Array[a, 25] (* Jean-Fran├žois Alcover, Nov 10 2017, after Vladeta Jovovic *)

CROSSREFS

Cf. A001787.

Cf. A084486, A055602, A055603.

Sequence in context: A121590 A186209 A005758 * A130072 A135158 A073382

Adjacent sequences:  A084482 A084483 A084484 * A084486 A084487 A084488

KEYWORD

nonn,easy

AUTHOR

W. Edwin Clark, May 27 2003

EXTENSIONS

Comment corrected by W. Edwin Clark, Sep 24 2012

STATUS

approved

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Last modified October 22 12:30 EDT 2019. Contains 328318 sequences. (Running on oeis4.)