cp's OEIS Frontend

A333667 Triangle T(n,k), n >= 2, 0 <= k <= floor(n^2/2)-2*n+2, read by rows, where T(n,k) is the number of 2*(k+2*n-2)-cycles in the n X n grid graph which pass through NW and SE corners ((0,0),(n-1,n-1)).

%I A333667 #26 Apr 02 2020 04:31:52
%S A333667 1,3,20,16,6,175,420,562,456,186,1764,8064,21224,39500,55376,57248,
%T A333667 37586,10260,1072,19404,138600,569768,1717152,4151965,8371428,
%U A333667 14126846,19364732,20241450,14759356,6998166,1927724,230440
%N A333667 Triangle T(n,k), n >= 2, 0 <= k <= floor(n^2/2)-2*n+2, read by rows, where T(n,k) is the number of 2*(k+2*n-2)-cycles in the n X n grid graph which pass through NW and SE corners ((0,0),(n-1,n-1)).
%H A333667 Seiichi Manyama, <a href="/A333667/b333667.txt">Rows n = 2..9, flattened</a>
%F A333667 T(n,0) = A000891(n-2).
%e A333667 T(3,0) = 3;
%e A333667    +--*--*   +--*--*   +--*
%e A333667    |     |   |     |   |  |
%e A333667    *--*  *   *     *   *  *--*
%e A333667       |  |   |     |   |     |
%e A333667       *--+   *--*--+   *--*--+
%e A333667 Triangle starts:
%e A333667 =======================================================================
%e A333667 n\k|      0        1         2 ...      4 ...   8 ...    12 ...     18
%e A333667 ---|-------------------------------------------------------------------
%e A333667 2  |      1;
%e A333667 3  |      3;
%e A333667 4  |     20,      16,        6;
%e A333667 5  |    175,     420,      562, ... , 186;
%e A333667 6  |   1764,    8064,    21224, .......... , 1072;
%e A333667 7  |  19404,  138600,   569768, .................. , 230440;
%e A333667 8  | 226512, 2265120, 12922446, ............................ , 4638576;
%o A333667 (Python)
%o A333667 # Using graphillion
%o A333667 from graphillion import GraphSet
%o A333667 import graphillion.tutorial as tl
%o A333667 def A333667(n):
%o A333667     universe = tl.grid(n - 1, n - 1)
%o A333667     GraphSet.set_universe(universe)
%o A333667     cycles = GraphSet.cycles().including(1).including(n * n)
%o A333667     return [cycles.len(2 * k).len() for k in range(2 * n - 2, n * n // 2 + 1)]
%o A333667 print([i for n in range(2, 8) for i in A333667(n)])
%Y A333667 Row sums give A333323.
%Y A333667 Cf. A003763, A302337, A333651, A333652, A333668.
%K A333667 nonn,tabf
%O A333667 2,2
%A A333667 _Seiichi Manyama_, Apr 01 2020