login
Number of non-attacking bishop positions on a cylindrical 3 X 2n chessboard.
3

%I #25 May 24 2019 02:02:43

%S 1,16,144,1156,11664,118336,1218816,12574116,129868816,1341610384,

%T 13860823824,143206237476,1479580304400,15286786268224,

%U 157940749232704,1631820172890436,16859722986240016,174192150898142224,1799727414404326416,18594516209802790084

%N Number of non-attacking bishop positions on a cylindrical 3 X 2n chessboard.

%H Ray Chandler, <a href="/A287168/b287168.txt">Table of n, a(n) for n = 0..986</a> (terms to 1000 digits)

%H Richard M. Low and Ardak Kapbasov, <a href="https://www.emis.de/journals/JIS/VOL20/Low/low2.html">Non-Attacking Bishop and King Positions on Regular and Cylindrical Chessboards</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.1, Table 11.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (14, -35, -48, 198, -112, -78, 72, -5, -6, 1).

%F G.f.: (-1 - 2 x + 45 x^2 + 252 x^3 - 1090 x^4 + 644 x^5 + 802 x^6 - 740 x^7 + 35 x^8 + 86 x^9 - 15 x^10) / (-1 + 14 x - 35 x^2 - 48 x^3 + 198 x^4 - 112 x^5 - 78 x^6 + 72 x^7 - 5 x^8 - 6 x^9 + x^10). [Corrected by _Georg Fischer_, May 23 2019]

%t CoefficientList[Series[(-1 - 2 x + 45 x^2 + 252 x^3 - 1090 x^4 + 644 x^5 + 802 x^6 - 740 x^7 + 35 x^8 + 86 x^9 - 15 x^10) / (-1 + 14 x - 35 x^2 - 48 x^3 + 198 x^4 - 112 x^5 - 78 x^6 + 72 x^7 - 5 x^8 - 6 x^9 + x^10), {x, 0, 986}], x] (* _Michael De Vlieger_, May 21 2017; simplified by _Georg Fischer_, May 23 2019 *)

%Y Cf. A286810, A287169.

%K nonn

%O 0,2

%A _Richard M. Low_, May 20 2017

%E More terms from _Michael De Vlieger_, May 21 2017