A243716 - OEIS

%I #7 Jun 15 2014 20:58:49

%S 1,1,2,1,1,3,7,9,6,2,3,18,40,66,49,30,8,3,6,43,195,609,1244,1767,1710,

%T 1148,510,154,31,6,1,6,83,618,3375,12329,32524,61731,86748,90059,

%U 70128,40770,18053,6089,1643,344,61,7,1,10,156,1751,14181,81900,348541

%N Irregular triangle read by rows: T(n, k) = number of inequivalent (mod the dihedral group D_8 of order 8) ways to place k nonattacking knights on an n X n board.

%C The triangle is irregularly shaped: 1 <= k <= A030978(n). A030978(n) is the maximal number of knights that can be placed on an n X n board.

%C First row corresponds to n = 1.

%C Counting "inequivalent ways" means: Rotations or reflections of a placement of knights on the board are considered to be the same placement.

%H Heinrich Ludwig, <a href="/A243716/b243716.txt">Table of n, a(n) for n = 1..116</a>

%e The triangle begins:

%e   1;

%e   1,  2,   1,   1;

%e   3,  7,   9,   6,    2;

%e   3, 18,  40,  66,   49,   30,    8,    3;

%e   6, 43, 195, 609, 1244, 1767, 1710, 1148, 510, 154, 31, 6, 1;

%e   ...

%Y Cf. A030978, A008805 (column 1), A243717 (column 2), A243718 (column 3), A243719 (column 4), A243720 (column 5).

%K nonn,tabf

%O 1,3

%A _Heinrich Ludwig_, Jun 10 2014