cp's OEIS Frontend

A240153 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one 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 A240153 #6 Jun 02 2025 09:40:45
%S A240153 2,3,3,4,5,4,7,8,11,7,10,19,20,25,10,15,36,107,67,62,15,24,57,186,676,
%T A240153 254,144,24,35,120,450,1328,3993,825,329,35,54,218,1641,5701,11742,
%U A240153 22412,2667,775,54,83,377,2788,24419,88214,108201,131005,8652,1781,83,124,758
%N A240153 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one 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 A240153 Table starts
%C A240153 ..2....3.....4........7.........10..........15..........24.........35
%C A240153 ..3....5.....8.......19.........36..........57.........120........218
%C A240153 ..4...11....20......107........186.........450........1641.......2788
%C A240153 ..7...25....67......676.......1328........5701.......24419......52676
%C A240153 .10...62...254.....3993......11742.......88214......536744....1652584
%C A240153 .15..144...825....22412.....108201.....1608415....12812998...70360014
%C A240153 .24..329..2667...131005....1056699....30542203...417799464.3795213209
%C A240153 .35..775..8652...731518...10526838...584983851.14482686630
%C A240153 .54.1781.27929..4144347..107361960.11643589675
%C A240153 .83.4150.91436.23263202.1116331018
%H A240153 R. H. Hardin, <a href="/A240153/b240153.txt">Table of n, a(n) for n = 1..112</a>
%F A240153 Empirical for column k:
%F A240153 k=1: a(n) = a(n-2) +2*a(n-3)
%F A240153 k=2: [order 34] for n>36
%F A240153 Empirical for row n:
%F A240153 n=1: a(n) = a(n-2) +2*a(n-3)
%F A240153 n=2: [order 17] for n>19
%e A240153 Some solutions for n=4 k=4
%e A240153 ..2..2..3..2....2..2..3..3....2..2..3..3....2..2..3..3....2..2..3..3
%e A240153 ..0..2..1..1....0..2..2..3....0..2..1..1....0..0..2..2....0..2..1..1
%e A240153 ..0..2..2..3....2..0..0..2....2..2..3..3....2..0..1..3....0..2..2..2
%e A240153 ..0..0..2..2....3..2..3..2....3..1..2..1....3..1..2..2....0..2..0..2
%Y A240153 Row and column 1 are A159288(n+1)
%K A240153 nonn,tabl
%O A240153 1,1
%A A240153 _R. H. Hardin_, Apr 02 2014