cp's OEIS Frontend

A036365 Number of chiral n-ominoes in n-2 space.

%I A036365 #15 Jan 13 2019 03:17:39
%S A036365 0,2,6,17,49,135,361,951,2493,6497,16837,43498,112164,288741,742294,
%T A036365 1906552,4893835,12555662,32201344,82566738,211675672,542621858,
%U A036365 1390929877,3565435302,9139718572,23430209922,60069035611,154014868677
%N A036365 Number of chiral n-ominoes in n-2 space.
%C A036365 a(n) is Lunnon's DR(n,n-2) - DE(n,n-2).
%H A036365 W. F. Lunnon, <a href="https://doi.org/10.1093/comjnl/18.4.366">Counting Multidimensional Polyominoes</a>, Computer Journal, Vol. 18 (1975), pp. 366-67.
%F A036365 G.f.: C^3(x)/2 + C(x)C(-x^2)/2 + 5C^4(x)/8 + C^2(x)C(-x^2)/4 + 3C^2(-x^2)/8 - C(-x^4)/4 + C^5(x)/(1-C(x)), where C(x) is the generating function for chiral n-ominoes in n-1 space, one cell labeled (that is, C(x) is the g.f. of the sequence A045648).
%e A036365 0 chiral trominoes in 1-space;
%e A036365 2 pairs of chiral tetrominoes (L,S) in 2-space;
%e A036365 6 pairs of chiral pentominoes in 3-space.
%t A036365 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;
%t A036365 c[ n_, 1 ] := c[ n, 1 ]=Sum[ c[ i, 1 ]sc[ n-1, i ]i, {i, 1, n-1} ]/(n-1);
%t A036365 c[ n_, k_ ] := c[ n, k ]=Sum[ c[ i, 1 ]c[ n-i, k-1 ], {i, 1, n-1} ];
%t A036365 Table[ c[ i, 3 ]/2+5c[ i, 4 ]/8+Sum[ c[ i, j ], {j, 5, i} ]+If[ OddQ[ i ], 0,
%t A036365 3c[ i/2, 2 ](-1)^(i/2)/8-If[ OddQ[ i/2 ], 0, c[ i/4, 1 ](-1)^(i/4)/4 ] ]
%t A036365 +Sum[ c[ j, 1 ](c[ i-2j, 1 ]/2+c[ i-2j, 2 ]/4)(-1)^j, {j, 1, (i-1)/2} ], {i, 3, 30} ]
%Y A036365 Cf. A045648, A045649, A036364.
%K A036365 easy,nice,nonn
%O A036365 3,2
%A A036365 _Robert A. Russell_