4,3

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

(C^2(x)+C(-x^2))^2/8-C^2(-x^2)/4-C(-x^4)/4 +C^5(x)/(2-2C(x)) +C(x)C^2(-x^2)/(2-2C(-x^2)) where C(x) is generating function for chiral n-ominoes in n-1 space, one cell labeled

4 pairs of chiral hexominoes in 2^4 space

sc[ n_, k_ ] := sc[ n, k ]=c[ n+1-k, 1 ]+If[ n<2k, 0, sc[ n-k, k ](-1)^k ]; c[ 1, 1 ] := 1;

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

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

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

c[ i/2, 2 ](-1)^(i/2)/8+If[ OddQ[ i/2 ], 0, c[ i/4, 1 ](-1)^(i/4)/4 ]

+Sum[ c[ i/2, j ](-1)^(i/2), {j, 3, i/2} ]/2 ]+Sum[ c[ j, 1 ]c[ i-2j, 2 ](-1)^j/4

-Sum[ If[ OddQ[ k ], c[ j, (k-1)/2 ]c[ i-2j, 1 ](-1)^j/2, 0 ], {k, 5, i} ],

{j, 1, (i-1)/2} ], {i, 4, 30} ]

Cf. A045648, A036367.

Adjacent sequences: A036365 A036366 A036367 this_sequence A036369 A036370 A036371

Sequence in context: A128758 A027166 A126943 this_sequence A006071 A086954 A111583

easy,nice,nonn

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