1,5

Eric Weisstein's World of Mathematics, Array

T(n, k) = 1/8*([n^2]_k+2*[n]_k+5*[0]_k) if n is even and 1/8*([n^2]_k+4*[n]_k+3*[1]_k) if n is odd, where [m]_k=m*(m-1)*...*(m-k+1), k>0, [m]_0=1, is falling factorial. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 10 2003

1,1; 1,1,2,3,3; 1,3,12,66,378,1890,7560,22680,45360,45360; ...

There is a single distinct 3 X 3 matrix containing all zeros, so a(3,1)=1.

There are 3 distinct 3 X 3 matrices containing a 1 and otherwise 0's, so a(3,2)=3.

There are 12 distinct 3 X 3 matrices containing a single 1, a single 2 and otherwise 0's, so a(3,3)=12.

There is a single distinct 3 X 3 matrix containing all zeros, so a(3, 0) = 1.

There are 3 distinct 3 X 3 matrices containing 8 0's and a 1, so a(3, 1) = 3.

There are 12 distinct 3 X 3 matrices containing a single 1, a single 2 and otherwise 0's, so a(3, 2) = 12.

(For 3 X 3 case) CanonicalizeArray[ x_ ] := Module[ {r, t}, Sort[ {x, Reverse[ x ], r=Reverse/@x, Reverse[ r ], t=Transpose[ x ], Reverse[ t ], r=Reverse/@t, Reverse[ r ]} ][ [ 1 ] ] ] ADD[ n_, d_ ] := Union[ CanonicalizeArray /@ (Partition[ #, n ] & /@ Permutations[ Join[ Range[ d ], Table[ 0, {n^2 - d} ] ] ]) ]

Cf. A086829, A085698.

Sequence in context: A051911 A106595 A109199 this_sequence A136453 A114104 A076780

Adjacent sequences: A087071 A087072 A087073 this_sequence A087075 A087076 A087077

nonn,tabf

Zakir Seidov (zakseidov(AT)yahoo.com) and Eric Weisstein (eric(AT)weisstein.com), Aug 08, 2003

More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Apr 12 2005