%I A036369
%S A036369 0,0,2,10,33,101,277,754,1972,5134,13145,33563,85048,215075,541887,
%T A036369 1363376,3423537,8588521,21522243,53898911,134895022,337467395,843924068,
%U A036369 2109897826,5273789335,13180026621,32934865984
%N A036369 Number of asymmetric orthoplex n-ominoes in n-2 space
%C A036369 Orthoplex polyominoes are multidimensional polyominoes that do not extend 
               more than two units along any axis.
%F A036369 (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.
%e A036369 2 asymmetric hexominoes in 2^4 space
%t A036369 sa[ n_, k_ ] := sa[ n, k ]=a[ n+1-k, 1 ]+If[ n<2k, 0, -sa[ n-k, k ] ]; 
               a[ 1, 1 ] := 1;
%t A036369 a[ n_, 1 ] := a[ n, 1 ]=Sum[ a[ i, 1 ]sa[ n-1, i ]i, {i, 1, n-1} ]/(n-1);
%t A036369 a[ n_, k_ ] := a[ n, k ]=Sum[ a[ i, 1 ]a[ n-i, k-1 ], {i, 1, n-1} ];
%t A036369 Table[ a[ i, 4 ]/8+Sum[ a[ i, j ], {j, 5, i} ]/2-If[ OddQ[ i ], 0, a[ 
               i/2, 2 ]/8
%t A036369 -If[ OddQ[ i/2 ], 0, a[ i/4, 1 ]/4 ]+Sum[ a[ i/2, j ], {j, 3, i/2} ]/
               2 ]
%t A036369 -Sum[ a[ j, 1 ]a[ i-2j, 2 ]/4+Sum[ If[ OddQ[ k ], a[ j,
%t A036369 (k-1)/2 ]a[ i-2j, 1 ], 0 ], {k, 5, i} ]/2, {j, 1, (i-1)/2} ], {i, 4, 
               30} ]
%Y A036369 Cf. A004111, A036366.
%Y A036369 Sequence in context: A004028 A080668 A062453 this_sequence A043004 A108100 
               A059924
%Y A036369 Adjacent sequences: A036366 A036367 A036368 this_sequence A036370 A036371 
               A036372
%K A036369 easy,nice,nonn
%O A036369 4,3
%A A036369 Robert A. Russell (russell(AT)post.harvard.edu)