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A240790 Number of n X 3 0..3 arrays with no element equal to one plus the sum of elements to its left or one 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 A240790 #8 Oct 30 2014 05:03:57
%S A240790 4,5,8,27,49,50,89,115,182,289,425,651,992,1486,2255,3349,5040,7706,
%T A240790 11754,17525,26365,39661,59893,89903,135336,203491,306233,460867,
%U A240790 692971,1040765,1565790,2353754,3540545,5319995,8000324,12027862,18084789
%N A240790 Number of n X 3 0..3 arrays with no element equal to one plus the sum of elements to its left or one 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 A240790 Column 3 of A240792.
%H A240790 R. H. Hardin, <a href="/A240790/b240790.txt">Table of n, a(n) for n = 1..210</a>
%F A240790 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>87.
%e A240790 Some solutions for n=4:
%e A240790 ..3..2..3....3..2..3....3..2..3....3..2..3....3..2..3....3..2..3....3..2..3
%e A240790 ..3..2..3....3..1..3....3..1..3....3..2..3....3..2..1....3..2..1....3..2..3
%e A240790 ..2..2..2....2..1..1....2..2..2....2..2..2....2..0..2....2..2..3....2..2..2
%e A240790 ..2..0..2....2..0..1....3..1..3....3..1..3....2..0..1....2..0..2....2..1..2
%Y A240790 Cf. A240792.
%K A240790 nonn
%O A240790 1,1
%A A240790 _R. H. Hardin_, Apr 12 2014