A287168 Number of non-attacking bishop positions on a cylindrical 3 X 2n chessboard.

1, 16, 144, 1156, 11664, 118336, 1218816, 12574116, 129868816, 1341610384, 13860823824, 143206237476, 1479580304400, 15286786268224, 157940749232704, 1631820172890436, 16859722986240016, 174192150898142224, 1799727414404326416, 18594516209802790084

Offset

0,2

Links

Ray Chandler, Table of n, a(n) for n = 0..986 (terms to 1000 digits)

Richard M. Low and Ardak Kapbasov, Non-Attacking Bishop and King Positions on Regular and Cylindrical Chessboards, Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.1, Table 11.

Index entries for linear recurrences with constant coefficients, signature (14, -35, -48, 198, -112, -78, 72, -5, -6, 1).

Formula

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]

Mathematica

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 *)

Crossrefs

Cf. A286810, A287169.

Sequence in context: A086952 A230971 A282524 * A155663 A077485 A131705

Adjacent sequences: A287165 A287166 A287167 * A287169 A287170 A287171

Keyword

nonn

Author

Richard M. Low, May 20 2017

Extensions

More terms from Michael De Vlieger, May 21 2017

Status

approved