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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 7

%I

%S 2,5,2,11,6,4,25,9,12,6,57,42,19,16,8,129,124,142,24,16,14,293,474,

%T 553,348,25,35,20,665,1440,4112,1750,653,35,35,30,1509,5239,18373,

%U 20657,5325,1809,45,36,48,3425,16730,131958,149324,77314,21859,3606,76,65,70,7773

%N 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 Table starts

%C ..2..5..11....25......57......129.......293........665........1509.......3425

%C ..2..6...9....42.....124......474......1440.......5239.......16730......58945

%C ..4.12..19...142.....553.....4112.....18373.....131958......625820....4472258

%C ..6.16..24...348....1750....20657....149324....1954881....16557694..232884150

%C ..8.16..25...653....5325....77314....947937...21847993...336059014.9470457699

%C .14.35..35..1809...21859...500139...9748926..420731038.11098085704

%C .20.35..45..3606...66809..2319189..75889699.5873834148

%C .30.36..76..8307..222091.11311246.583512422

%C .48.65.117.20609..811643.62333325

%C .70.83.180.42658.2448916

%H R. H. Hardin, <a href="/A240760/b240760.txt">Table of n, a(n) for n = 1..109</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-2) +2*a(n-3)

%F 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 k=3: [order 76] for n>84

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)

%e Some solutions for n=4 k=4

%e ..3..3..1..1....2..2..2..2....3..3..1..3....2..1..1..3....2..2..3..3

%e ..2..0..2..3....3..3..1..1....2..0..0..2....3..3..0..2....3..1..0..2

%e ..2..0..2..3....3..2..0..1....3..1..0..2....2..1..3..2....2..0..1..3

%e ..2..0..0..2....2..0..2..2....3..1..0..2....2..0..1..2....2..0..1..3

%Y Column 1 is A239851

%Y Row 1 is A239812

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 12 2014

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Last modified January 26 19:15 EST 2022. Contains 350599 sequences. (Running on oeis4.)