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
Keywords
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).
Programs
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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 *)
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]
Extensions
More terms from Michael De Vlieger, May 21 2017