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A240757 Number of n X 3 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of 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.

%I A240757 #6 Mar 08 2023 13:43:40
%S A240757 11,9,19,24,25,35,45,76,117,180,265,365,533,786,1220,1796,2728,4087,
%T A240757 6140,9060,13625,20484,30734,46161,69561,104127,156807,235060,353693,
%U A240757 530499,798289,1200045,1804325,2711062,4074989,6123683,9207099,13837742
%N A240757 Number of n X 3 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of 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 A240757 Column 3 of A240760.
%H A240757 R. H. Hardin, <a href="/A240757/b240757.txt">Table of n, a(n) for n = 1..210</a>
%F A240757 Empirical: a(n) = 5*a(n-5) +4*a(n-6) +a(n-7) +4*a(n-8) +5*a(n-9) -6*a(n-10) -12*a(n-11) -a(n-12) -13*a(n-13) -16*a(n-14) -7*a(n-15) +13*a(n-16) +2*a(n-17) +20*a(n-18) +24*a(n-19) +15*a(n-20) -3*a(n-21) -2*a(n-22) -20*a(n-23) -44*a(n-24) -11*a(n-25) +9*a(n-26) -82*a(n-27) -30*a(n-28) +19*a(n-29) -21*a(n-30) -108*a(n-31) +132*a(n-32) +43*a(n-33) -68*a(n-34) +17*a(n-35) +171*a(n-36) -171*a(n-37) +66*a(n-38) +206*a(n-39) -46*a(n-40) -124*a(n-41) +214*a(n-42) -29*a(n-43) -283*a(n-44) +123*a(n-45) +129*a(n-46) -251*a(n-47) -6*a(n-48) +164*a(n-49) -17*a(n-50) -121*a(n-51) +216*a(n-52) +51*a(n-53) -79*a(n-54) +40*a(n-55) +58*a(n-56) -21*a(n-57) -16*a(n-58) +32*a(n-59) -3*a(n-60) -47*a(n-61) -29*a(n-62) -9*a(n-63) -2*a(n-64) -11*a(n-65) -2*a(n-66) +10*a(n-67) -6*a(n-69) +12*a(n-70) +3*a(n-71) -4*a(n-72) -3*a(n-73) +3*a(n-74) +a(n-75) -3*a(n-76) for n>84.
%e A240757 Some solutions for n=4
%e A240757 ..2..2..2....2..2..2....2..2..2....3..1..3....2..1..1....3..1..3....2..2..2
%e A240757 ..3..3..1....3..3..1....3..1..3....2..2..2....3..3..2....2..2..2....3..3..1
%e A240757 ..2..0..2....2..2..2....2..0..2....3..1..2....2..1..2....2..1..3....2..2..2
%e A240757 ..2..0..2....2..1..3....2..0..1....2..1..2....2..0..2....2..1..2....2..1..2
%Y A240757 Cf. A240760.
%K A240757 nonn
%O A240757 1,1
%A A240757 _R. H. Hardin_, Apr 12 2014