4,3

Orthoplex polyominoes are multidimensional polyominoes that do not extend more than two units along any axis.

(A^2(x)-A(x^2))^2/8-A^2(x^2)/4+A(x^4)/4 +A^5(x)/(2-2A(x)) -A(x)A^2(x^2)/(2-2A(x^2)) where A(x) is generating function for rooted identity trees with n nodes.

2 asymmetric hexominoes in 2^4 space

sa[ n_, k_ ] := sa[ n, k ]=a[ n+1-k, 1 ]+If[ n<2k, 0, -sa[ n-k, k ] ]; a[ 1, 1 ] := 1;

a[ n_, 1 ] := a[ n, 1 ]=Sum[ a[ i, 1 ]sa[ n-1, i ]i, {i, 1, n-1} ]/(n-1);

a[ n_, k_ ] := a[ n, k ]=Sum[ a[ i, 1 ]a[ n-i, k-1 ], {i, 1, n-1} ];

Table[ a[ i, 4 ]/8+Sum[ a[ i, j ], {j, 5, i} ]/2-If[ OddQ[ i ], 0, a[ i/2, 2 ]/8

-If[ OddQ[ i/2 ], 0, a[ i/4, 1 ]/4 ]+Sum[ a[ i/2, j ], {j, 3, i/2} ]/2 ]

-Sum[ a[ j, 1 ]a[ i-2j, 2 ]/4+Sum[ If[ OddQ[ k ], a[ j,

(k-1)/2 ]a[ i-2j, 1 ], 0 ], {k, 5, i} ]/2, {j, 1, (i-1)/2} ], {i, 4, 30} ]

Cf. A004111, A036366.

Sequence in context: A004028 A080668 A062453 this_sequence A043004 A108100 A059924

Adjacent sequences: A036366 A036367 A036368 this_sequence A036370 A036371 A036372

easy,nice,nonn

Robert A. Russell (russell(AT)post.harvard.edu)