cp's OEIS Frontend

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.

%I A241356 #8 Apr 26 2021 19:29:56
%S A241356 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 A241356 24,30,103,230,228,248,124,7,35,48,160,641,1721,615,624,243,8,54,70,
%U A241356 344,960,5663,6307,2062,1323,370,9,83,108,643,3746,11909,32942,35880,6380,2715
%N 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.
%C A241356 Table starts
%C A241356 ..2..2...4.....6......8.......14........20.........30.........48.........70
%C A241356 ..3..3...9....17.....23.......53.......103........160........344........643
%C A241356 ..4..3..19....51.....61......230.......641........960.......3746.......9339
%C A241356 ..7..4..55...128....228.....1721......5663......11909......69946.....220363
%C A241356 .10..5..72...248....615.....6307.....32942......81541.....704210....3476469
%C A241356 .15..5.124...624...2062....35880....247664.....921726...10840453...85630246
%C A241356 .24..7.243..1323...6380...183400...1904754...10693549..198803445.2384535274
%C A241356 .35..8.370..2715..17325...763750..12340892..109041097.3042023002
%C A241356 .54..9.695..5798..60671..4110488.104529676.1490516896
%C A241356 .83.12.956.11469.174659.18352240.729080777
%H A241356 R. H. Hardin, <a href="/A241356/b241356.txt">Table of n, a(n) for n = 1..143</a>
%F A241356 Empirical for column k:
%F A241356 k=1: a(n) = a(n-2) +2*a(n-3).
%F A241356 k=2: a(n) = a(n-3) +a(n-5).
%F A241356 k=3: [order 68] for n > 85.
%F A241356 Empirical for row n:
%F A241356 n=1: a(n) = a(n-2) +2*a(n-3).
%F A241356 n=2: [order 17] for n > 20.
%e A241356 Some solutions for n=4, k=4
%e A241356 ..3..2..3..3....3..2..3..3....3..2..3..3....3..2..3..3....3..2..3..3
%e A241356 ..3..1..1..2....3..1..1..3....3..1..2..1....3..1..2..1....3..1..2..1
%e A241356 ..2..1..0..1....2..1..0..1....2..3..0..3....2..3..3..3....2..3..0..3
%e A241356 ..3..0..2..2....3..2..3..2....3..0..1..3....2..1..0..1....3..2..0..2
%Y A241356 Column 1 is A159288(n+1).
%Y A241356 Column 2 is A226503(n+8).
%Y A241356 Row 1 is A239851.
%K A241356 nonn,tabl
%O A241356 1,1
%A A241356 _R. H. Hardin_, Apr 20 2014