cp's OEIS Frontend

A223062 T(n,k)=Number of nXk 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.

%I A223062 #6 Jul 23 2025 03:26:56
%S A223062 1,2,2,5,10,5,15,114,114,15,51,1473,4865,1473,51,187,19360,213469,
%T A223062 213469,19360,187,715,255045,9383963,31331820,9383963,255045,715,2795,
%U A223062 3361024,412602889,4606719559,4606719559,412602889,3361024,2795,11051,44294253
%N A223062 T(n,k)=Number of nXk 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.
%C A223062 Table starts
%C A223062 ...1......2.........5...........15...............51.................187
%C A223062 ...2.....10.......114.........1473............19360..............255045
%C A223062 ...5....114......4865.......213469..........9383963...........412602889
%C A223062 ..15...1473....213469.....31331820.......4606719559........677531592132
%C A223062 ..51..19360...9383963...4606719559....2266567594841....1115636153544055
%C A223062 .187.255045.412602889.677531592132.1115636153544055.1837966217755803448
%H A223062 R. H. Hardin, <a href="/A223062/b223062.txt">Table of n, a(n) for n = 1..127</a>
%F A223062 Empirical for column k:
%F A223062 k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)
%F A223062 k=2: a(n) = 18*a(n-1) -71*a(n-2) +102*a(n-3) -48*a(n-4) for n>5
%F A223062 k=3: a(n) = 55*a(n-1) -515*a(n-2) +1337*a(n-3) -696*a(n-4) -1188*a(n-5) +1008*a(n-6) for n>7
%F A223062 k=4: [order 11 for n>12]
%e A223062 Some solutions for n=3 k=4
%e A223062 ..0..1..0..1....0..1..0..2....0..1..0..2....0..1..0..1....0..1..1..0
%e A223062 ..2..2..0..1....2..1..0..2....2..3..0..2....2..1..2..2....0..2..3..0
%e A223062 ..3..3..3..3....2..3..1..0....2..1..2..0....3..2..3..0....0..2..0..1
%Y A223062 Column 1 is A007581(n-1)
%K A223062 nonn,tabl
%O A223062 1,2
%A A223062 _R. H. Hardin_ Mar 13 2013