cp's OEIS Frontend

A220553 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

%I A220553 #6 Jul 23 2025 01:13:01
%S A220553 1,2,2,3,8,3,5,29,29,5,8,108,224,108,8,13,401,1814,1814,401,13,21,
%T A220553 1490,14556,32173,14556,1490,21,34,5536,117022,565061,565061,117022,
%U A220553 5536,34,55,20569,940432,9943416,21668208,9943416,940432,20569,55,89,76424
%N A220553 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.
%C A220553 Table starts
%C A220553 ...1.......2...........3...............5...................8
%C A220553 ...2.......8..........29.............108.................401
%C A220553 ...3......29.........224............1814...............14556
%C A220553 ...5.....108........1814...........32173..............565061
%C A220553 ...8.....401.......14556..........565061............21668208
%C A220553 ..13....1490......117022.........9943416...........832899775
%C A220553 ..21....5536......940432.......174911750.........32001129185
%C A220553 ..34...20569.....7558245......3077034244.......1229633337183
%C A220553 ..55...76424....60744605.....54130248568......47247493674864
%C A220553 ..89..283953...488197825....952245176313....1815445803499208
%C A220553 .144.1055026..3923590632..16751640356635...69756959373004005
%C A220553 .233.3919944.31533457665.294690365449276.2680352078247056300
%H A220553 R. H. Hardin, <a href="/A220553/b220553.txt">Table of n, a(n) for n = 1..312</a>
%e A220553 Some solutions for n=3 k=4 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
%e A220553 ..8..8..0..7....0..6..4..0....0..0..6..4....6..4..7..0....0..0..0..0
%e A220553 ..2..2..3..0....0..7..0..7....0..0..6..4....0..3..8..0....8..0..0..8
%e A220553 ..0..0..6..4....3..0..3..0....0..0..6..4....0..0..2..0....2..6..4..2
%Y A220553 Column 1 is A000045(n+1)
%K A220553 nonn,tabl
%O A220553 1,2
%A A220553 _R. H. Hardin_ Dec 15 2012