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A220562 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal or antidiagonal neighbor.

%I A220562 #6 Jul 23 2025 01:13:36
%S A220562 1,2,1,3,5,1,5,14,13,1,8,47,64,34,1,13,149,430,292,89,1,21,481,2604,
%T A220562 3966,1332,233,1,34,1544,16310,45966,36640,6076,610,1,55,4965,101052,
%U A220562 561636,810778,338581,27716,1597,1,89,15957,628269,6743873,19333688,14298089
%N A220562 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal or antidiagonal neighbor.
%C A220562 Table starts
%C A220562 .1.....2........3............5...............8..................13
%C A220562 .1.....5.......14...........47.............149.................481
%C A220562 .1....13.......64..........430............2604...............16310
%C A220562 .1....34......292.........3966...........45966..............561636
%C A220562 .1....89.....1332........36640..........810778............19333688
%C A220562 .1...233.....6076.......338581........14298089...........665748170
%C A220562 .1...610....27716......3128843.......252139015.........22926570957
%C A220562 .1..1597...126428.....28913910......4446314533........789539775889
%C A220562 .1..4181...576708....267196106.....78407942556......27190037181789
%C A220562 .1.10946..2630684...2469184016...1382674335890.....936366170726784
%C A220562 .1.28657.12000004..22817958901..24382584703194...32246430390993213
%C A220562 .1.75025.54738652.210862878471.429971411669361.1110497486239608510
%H A220562 R. H. Hardin, <a href="/A220562/b220562.txt">Table of n, a(n) for n = 1..337</a>
%e A220562 Some solutions for n=3 k=4 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
%e A220562 ..0..0..0..0....0..6..4..0....0..7..6..4....0..7..6..4....6..4..0..0
%e A220562 ..0..7..6..4....6..4..7..0....3..0..0..0....3..0..0..7....6..4..7..7
%e A220562 ..3..6..4..0....0..3..0..0....0..0..0..0....0..0..3..0....0..3..3..0
%Y A220562 Column 2 is A001519(n+1)
%Y A220562 Column 3 is A060801
%Y A220562 Row 1 is A000045(n+1)
%K A220562 nonn,tabl
%O A220562 1,2
%A A220562 _R. H. Hardin_ Dec 16 2012