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A287168
Number of non-attacking bishop positions on a cylindrical 3 X 2n chessboard.
3
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
Sequence in context: A086952 A230971 A282524 * A155663 A077485 A131705
KEYWORD
nonn
AUTHOR
Richard M. Low, May 20 2017
EXTENSIONS
More terms from Michael De Vlieger, May 21 2017
STATUS
approved