cp's OEIS Frontend

A241306 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

%I A241306 #6 Jun 02 2025 10:05:07
%S A241306 2,2,5,4,6,11,6,15,6,25,8,25,37,12,57,14,40,74,116,16,129,20,89,186,
%T A241306 330,304,28,293,30,121,646,1462,1145,869,38,665,48,237,1278,5757,6718,
%U A241306 4499,2398,66,1509,70,390,3418,22343,49918,41336,15827,6813,92,3425,108,682
%N A241306 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.
%C A241306 Table starts
%C A241306 ....2...2.....4......6........8.........14..........20..........30..........48
%C A241306 ....5...6....15.....25.......40.........89.........121.........237.........390
%C A241306 ...11...6....37.....74......186........646........1278........3418........9113
%C A241306 ...25..12...116....330.....1462.......5757.......22343.......79043......304799
%C A241306 ...57..16...304...1145.....6718......49918......283985.....1666242.....9581018
%C A241306 ..129..28...869...4499....41336.....490486.....5098814....41458261...447396605
%C A241306 ..293..38..2398..15827...217785....3893262....70316883...978925384.16677156613
%C A241306 ..665..66..6813..58043..1215485...37039909..1194164944.30759996872
%C A241306 .1509..92.18782.209838..6526016..307030328.16586413847
%C A241306 .3425.154.53067.757771.35833494.2801405991
%H A241306 R. H. Hardin, <a href="/A241306/b241306.txt">Table of n, a(n) for n = 1..126</a>
%F A241306 Empirical for column k:
%F A241306 k=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
%F A241306 k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-5)
%F A241306 Empirical for row n:
%F A241306 n=1: a(n) = a(n-2) +2*a(n-3)
%F A241306 n=2: [order 14] for n>20
%e A241306 Some solutions for n=4 k=4
%e A241306 ..3..2..3..2....3..2..3..2....3..2..3..3....3..2..3..2....3..2..2..2
%e A241306 ..1..2..1..1....3..1..3..1....1..2..1..1....1..2..1..1....3..0..0..1
%e A241306 ..2..0..0..1....1..2..2..3....3..2..2..2....3..2..0..2....1..0..2..1
%e A241306 ..1..0..3..3....2..0..0..1....1..2..0..2....2..0..0..3....1..0..0..2
%Y A241306 Column 1 is A239812
%Y A241306 Row 1 is A239851
%K A241306 nonn,tabl
%O A241306 1,1
%A A241306 _R. H. Hardin_, Apr 18 2014