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 A054867 Number of non-attacking configurations on a diamond of size n, where a prince attacks the four adjacent non-diagonal squares. 3
 1, 2, 17, 689, 139344, 142999897, 748437606081, 19999400591072512, 2728539172202554958697, 1900346273206544901717879089, 6755797872872106084596492075448192, 122584407857548123729431742141838309441329, 11352604691637658946858196503018301306800588837281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A diamond of size n X n contains (n^2 + (n-1)^2) = A001844(n-1) squares. For n > 0, a(n) is the number of ways to place non-adjacent counters on the black squares of a 2n-1 X 2n-1 checker board. The checker board is such that the black squares are in the corners. - Andrew Howroyd, Jan 16 2020 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..20 Eric Weisstein's World of Mathematics, Independent Vertex Set EXAMPLE From Andrew Howroyd, Jan 16 2020: (Start) Case n=2: The grid consists of 5 squares as shown below. __ __|__|__ |__|__|__| |__| If a prince is placed on the central square then a prince cannot be placed on the other 4 squares, otherwise princes can be placed in any combination. The total number of non-attacking configurations is then 1 + 2^4 = 17, so a(2) = 17. . Case n=3: The grid consists of 13 squares as shown below: __ __|__|__ __|__|__|__|__ |__|__|__|__|__| |__|__|__| |__| The total number of non-attacking configurations of princes is 689 so a(3) = 689. (End) CROSSREFS Main diagonal of A331406. Cf. A006506, A001844. Sequence in context: A013094 A013063 A012992 * A268270 A167436 A015189 Adjacent sequences: A054864 A054865 A054866 * A054868 A054869 A054870 KEYWORD hard,nonn AUTHOR Matti De Craene (Matti.DeCraene(AT)rug.ac.be), May 14 2000 EXTENSIONS a(0)=1 prepended and terms a(5) and beyond from Andrew Howroyd, Jan 15 2020 STATUS approved

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Last modified December 1 09:16 EST 2023. Contains 367471 sequences. (Running on oeis4.)