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A239030 T(n,k)=Number of nXk 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

%I A239030 #6 Jun 02 2025 09:23:13
%S A239030 1,1,2,1,3,2,1,4,4,4,1,5,7,11,4,1,6,11,28,16,8,1,7,16,59,54,43,8,1,8,
%T A239030 22,110,149,212,64,16,1,9,29,189,354,806,428,171,16,1,10,37,306,757,
%U A239030 2592,2195,1652,256,32,1,11,46,473,1495,7265,9319,11768,3410,683,32,1,12,56
%N A239030 T(n,k)=Number of nXk 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.
%C A239030 Table starts
%C A239030 ..1...1.....1......1.......1........1.........1.........1..........1
%C A239030 ..2...3.....4......5.......6........7.........8.........9.........10
%C A239030 ..2...4.....7.....11......16.......22........29........37.........46
%C A239030 ..4..11....28.....59.....110......189.......306.......473........704
%C A239030 ..4..16....54....149.....354......757......1495......2773.......4888
%C A239030 ..8..43...212....806....2592.....7265.....18362.....42809......93464
%C A239030 ..8..64...428...2195....9319....33699....107611....311585.....833304
%C A239030 .16.171..1652..11768...69288...339315...1435014...5388959...18371174
%C A239030 .16.256..3410..33417..265247..1719471...9453266..45358859..194626082
%C A239030 .32.683.13004.177087.1965398.17562449.131139508.838702960.4711005062
%H A239030 R. H. Hardin, <a href="/A239030/b239030.txt">Table of n, a(n) for n = 1..480</a>
%F A239030 Empirical for column k:
%F A239030 k=1: a(n) = 2*a(n-2)
%F A239030 k=2: a(n) = 5*a(n-2) -4*a(n-4)
%F A239030 k=3: a(n) = 17*a(n-2) -96*a(n-4) +210*a(n-6) -152*a(n-8)
%F A239030 k=4: [order 18]
%F A239030 k=5: [order 38]
%F A239030 k=6: [order 90]
%F A239030 Empirical for row n:
%F A239030 n=1: a(n) = 1
%F A239030 n=2: a(n) = n + 1
%F A239030 n=3: a(n) = (1/2)*n^2 + (1/2)*n + 1
%F A239030 n=4: a(n) = (1/12)*n^4 - (1/6)*n^3 + (47/12)*n^2 - (29/6)*n + 5
%F A239030 n=5: [polynomial of degree 6] for n>1
%F A239030 n=6: [polynomial of degree 9] for n>2
%F A239030 n=7: [polynomial of degree 12] for n>3
%e A239030 Some solutions for n=5 k=4
%e A239030 ..2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0
%e A239030 ..2..0..0..0....1..2..2..0....2..0..0..0....1..0..2..2....1..2..2..0
%e A239030 ..1..0..2..2....2..1..2..0....1..0..2..2....2..0..1..2....2..1..2..0
%e A239030 ..2..0..1..1....2..0..1..2....1..0..2..1....2..0..0..1....2..0..1..2
%e A239030 ..1..0..2..2....1..0..2..2....2..0..0..0....1..0..2..1....1..2..2..1
%Y A239030 Column 1 is A016116
%Y A239030 Row 2 is A000027(n+1)
%Y A239030 Row 3 is A000124
%K A239030 nonn,tabl
%O A239030 1,3
%A A239030 _R. H. Hardin_, Mar 09 2014