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A241356 T(n,k) = Number of n X k 0..3 arrays with no element equal to zero 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. 13

%I #8 Apr 26 2021 19:29:56

%S 2,2,3,4,3,4,6,9,3,7,8,17,19,4,10,14,23,51,55,5,15,20,53,61,128,72,5,

%T 24,30,103,230,228,248,124,7,35,48,160,641,1721,615,624,243,8,54,70,

%U 344,960,5663,6307,2062,1323,370,9,83,108,643,3746,11909,32942,35880,6380,2715

%N T(n,k) = Number of n X k 0..3 arrays with no element equal to zero 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 Table starts

%C ..2..2...4.....6......8.......14........20.........30.........48.........70

%C ..3..3...9....17.....23.......53.......103........160........344........643

%C ..4..3..19....51.....61......230.......641........960.......3746.......9339

%C ..7..4..55...128....228.....1721......5663......11909......69946.....220363

%C .10..5..72...248....615.....6307.....32942......81541.....704210....3476469

%C .15..5.124...624...2062....35880....247664.....921726...10840453...85630246

%C .24..7.243..1323...6380...183400...1904754...10693549..198803445.2384535274

%C .35..8.370..2715..17325...763750..12340892..109041097.3042023002

%C .54..9.695..5798..60671..4110488.104529676.1490516896

%C .83.12.956.11469.174659.18352240.729080777

%H R. H. Hardin, <a href="/A241356/b241356.txt">Table of n, a(n) for n = 1..143</a>

%F Empirical for column k:

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

%F k=2: a(n) = a(n-3) +a(n-5).

%F k=3: [order 68] for n > 85.

%F Empirical for row n:

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

%F n=2: [order 17] for n > 20.

%e Some solutions for n=4, k=4

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

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

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

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

%Y Column 1 is A159288(n+1).

%Y Column 2 is A226503(n+8).

%Y Row 1 is A239851.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 20 2014

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Last modified March 4 12:45 EST 2024. Contains 370532 sequences. (Running on oeis4.)