cp's OEIS Frontend

A240000 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

%I A240000 #6 Jun 02 2025 09:37:25
%S A240000 2,3,5,4,13,12,5,25,61,28,6,42,190,256,66,7,65,526,1372,1117,156,8,95,
%T A240000 1262,6527,10405,5012,368,9,133,2766,27415,86360,83029,22592,868,10,
%U A240000 180,5647,104291,635873,1225281,685898,102336,2048,11,237,10878,363859
%N A240000 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.
%C A240000 Table starts
%C A240000 ....2.......3.........4...........5............6............7............8
%C A240000 ....5......13........25..........42...........65...........95..........133
%C A240000 ...12......61.......190.........526.........1262.........2766.........5647
%C A240000 ...28.....256......1372........6527........27415.......104291.......363859
%C A240000 ...66....1117.....10405.......86360.......635873......4267171.....26152051
%C A240000 ..156....5012.....83029.....1225281.....15981219....191691132...2090236137
%C A240000 ..368...22592....685898....18392485....429788876...9314138750.182333502325
%C A240000 ..868..102336...5825700...290513038..12392346376.491124025940
%C A240000 .2048..465662..50417154..4767970186.378942837634
%C A240000 .4832.2123857.441675344.80410934960
%H A240000 R. H. Hardin, <a href="/A240000/b240000.txt">Table of n, a(n) for n = 1..98</a>
%F A240000 Empirical for column k:
%F A240000 k=1: a(n) = 2*a(n-1) +2*a(n-3)
%F A240000 k=2: [order 26]
%F A240000 Empirical for row n:
%F A240000 n=1: a(n) = n + 1
%F A240000 n=2: a(n) = (1/6)*n^3 + 1*n^2 + (23/6)*n
%F A240000 n=3: [polynomial of degree 8] for n>6
%F A240000 n=4: [polynomial of degree 19] for n>20
%F A240000 n=5: [polynomial of degree 44] for n>52
%e A240000 Some solutions for n=4 k=4
%e A240000 ..0..3..3..0....0..0..3..3....3..3..0..0....3..3..0..0....0..0..0..0
%e A240000 ..0..0..2..1....0..3..2..3....2..2..3..3....0..3..1..3....3..3..0..0
%e A240000 ..3..3..0..0....0..0..2..2....2..0..0..0....3..3..1..2....3..3..1..3
%e A240000 ..2..1..2..0....0..3..2..3....3..1..0..0....2..2..2..1....3..3..2..2
%Y A240000 Column 1 is A239333
%K A240000 nonn,tabl
%O A240000 1,1
%A A240000 _R. H. Hardin_, Mar 30 2014