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 A342372 Triangle T(n,k) of number of ways of arranging q nonattacking semi-queens on an n X n toroidal board, where 0 <= k <= n. 1
 1, 1, 1, 1, 4, 0, 1, 9, 9, 3, 1, 16, 48, 32, 0, 1, 25, 150, 250, 75, 15, 1, 36, 360, 1200, 1224, 288, 0, 1, 49, 735, 4165, 8869, 6321, 931, 133, 1, 64, 1344, 11648, 43136, 64512, 33024, 4096, 0, 1, 81, 2268, 27972, 160866, 423306, 469800 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS T(0,0):=1 for combinatorial reasons. A semi-queen can only move horizontal, vertical and parallel to the main diagonal of the board. Moves parallel to the secondary diagonal are not allowed. Instead of a board on a torus, you can imagine that the semi-queens can leave a flat board on one side and re-enter the board on the other side. LINKS Walter Trump, Table of n, a(n) for n = 1..222 Walter Trump, Semi-queen problem FORMULA T(n,0) = 1. T(n,1) = n^2. T(n,2) = n^2*(n-1)*(n-2)/2. T(n,3) = n^2*(n-1)*(n-2)*(n^2-6n+10)/6. T(2n+1,2n+1) = A006717(n). T(2n,2n) = 0. EXAMPLE 1;   1,  1;   1,  4,   0;   1,  9,   9,   3;   1, 16,  48,  32,  0;   1, 25, 150, 250, 75, 15; CROSSREFS Cf. A006717, A099152, A103220, A202654, A202655, A202656, A202657. Sequence in context: A186761 A199786 A189245 * A289222 A121301 A059056 Adjacent sequences:  A342369 A342370 A342371 * A342373 A342374 A342375 KEYWORD tabl,nonn AUTHOR Walter Trump, Mar 09 2021 STATUS approved

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Last modified July 30 15:29 EDT 2021. Contains 346359 sequences. (Running on oeis4.)