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A240760 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or zero 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 A240760 #6 Jun 02 2025 09:59:33
%S A240760 2,5,2,11,6,4,25,9,12,6,57,42,19,16,8,129,124,142,24,16,14,293,474,
%T A240760 553,348,25,35,20,665,1440,4112,1750,653,35,35,30,1509,5239,18373,
%U A240760 20657,5325,1809,45,36,48,3425,16730,131958,149324,77314,21859,3606,76,65,70,7773
%N A240760 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or zero 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 A240760 Table starts
%C A240760 ..2..5..11....25......57......129.......293........665........1509.......3425
%C A240760 ..2..6...9....42.....124......474......1440.......5239.......16730......58945
%C A240760 ..4.12..19...142.....553.....4112.....18373.....131958......625820....4472258
%C A240760 ..6.16..24...348....1750....20657....149324....1954881....16557694..232884150
%C A240760 ..8.16..25...653....5325....77314....947937...21847993...336059014.9470457699
%C A240760 .14.35..35..1809...21859...500139...9748926..420731038.11098085704
%C A240760 .20.35..45..3606...66809..2319189..75889699.5873834148
%C A240760 .30.36..76..8307..222091.11311246.583512422
%C A240760 .48.65.117.20609..811643.62333325
%C A240760 .70.83.180.42658.2448916
%H A240760 R. H. Hardin, <a href="/A240760/b240760.txt">Table of n, a(n) for n = 1..109</a>
%F A240760 Empirical for column k:
%F A240760 k=1: a(n) = a(n-2) +2*a(n-3)
%F A240760 k=2: a(n) = 3*a(n-3) +a(n-5) -2*a(n-8) -4*a(n-9) -a(n-11) +2*a(n-14) for n>17
%F A240760 k=3: [order 76] for n>84
%F A240760 Empirical for row n:
%F A240760 n=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
%e A240760 Some solutions for n=4 k=4
%e A240760 ..3..3..1..1....2..2..2..2....3..3..1..3....2..1..1..3....2..2..3..3
%e A240760 ..2..0..2..3....3..3..1..1....2..0..0..2....3..3..0..2....3..1..0..2
%e A240760 ..2..0..2..3....3..2..0..1....3..1..0..2....2..1..3..2....2..0..1..3
%e A240760 ..2..0..0..2....2..0..2..2....3..1..0..2....2..0..1..2....2..0..1..3
%Y A240760 Column 1 is A239851
%Y A240760 Row 1 is A239812
%K A240760 nonn,tabl
%O A240760 1,1
%A A240760 _R. H. Hardin_, Apr 12 2014