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 A239986 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4 13
 1, 1, 2, 1, 3, 3, 1, 4, 6, 4, 1, 5, 13, 16, 7, 1, 6, 22, 56, 40, 10, 1, 7, 38, 171, 261, 84, 15, 1, 8, 65, 530, 1391, 935, 208, 24, 1, 9, 107, 1495, 7113, 9079, 4113, 474, 35, 1, 10, 169, 4059, 31226, 83658, 70107, 16724, 1047, 54, 1, 11, 257, 10121, 131242, 652346 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ..1....1......1........1..........1............1............1............1 ..2....3......4........5..........6............7............8............9 ..3....6.....13.......22.........38...........65..........107..........169 ..4...16.....56......171........530.........1495.........4059........10121 ..7...40....261.....1391.......7113........31226.......131242.......514539 .10...84....935.....9079......83658.......652346......4803152.....33097266 .15..208...4113....70107....1174822.....16721012....226886115...2823199343 .24..474..16724...514297...15307425....381369904...9004871354.198719581101 .35.1047..63746..3533132..192702130...9009351655.404795616742 .54.2530.275188.27478686.2733573580.233083355837 LINKS R. H. Hardin, Table of n, a(n) for n = 1..128 FORMULA Empirical for column k: k=1: a(n) = a(n-2) +2*a(n-3) k=2: a(n) = 2*a(n-2) +10*a(n-3) -a(n-4) -5*a(n-5) -15*a(n-6) +a(n-7) +4*a(n-8) +2*a(n-9) +10*a(n-10) +5*a(n-11) -6*a(n-13) Empirical for row n: n=1: a(n) = 1 n=2: a(n) = n + 1 n=3: a(n) = (1/24)*n^4 - (1/4)*n^3 + (71/24)*n^2 - (43/4)*n + 23 for n>3 n=4: [polynomial of degree 10] for n>12 n=5: [polynomial of degree 24] for n>31 n=6: [polynomial of degree 55] for n>73 EXAMPLE Some solutions for n=4 k=4 ..3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0 ..3..1..3..0....2..3..0..3....3..1..3..0....2..1..0..0....2..1..0..0 ..3..1..2..1....2..0..1..2....3..2..0..3....2..0..3..3....2..0..3..0 ..2..1..0..0....3..0..0..1....2..3..0..3....3..2..2..2....2..0..0..3 CROSSREFS Column 1 is A159288 Sequence in context: A075195 A293311 A126885 * A285548 A130305 A323346 Adjacent sequences:  A239983 A239984 A239985 * A239987 A239988 A239989 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 30 2014 STATUS approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)