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A241056 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

%I A241056 #6 Jun 02 2025 10:01:13
%S A241056 4,4,3,24,60,93,297,507,1264,2850,6180,15453,33463,81394,185671,
%T A241056 428769,1005669,2301449,5384371,12403537,28828484,66828140,154614938,
%U A241056 359224400,831157978,1928175521,4468984943,10355201708,24011010277,55638167866
%N A241056 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.
%C A241056 Row 3 of A241054
%H A241056 R. H. Hardin, <a href="/A241056/b241056.txt">Table of n, a(n) for n = 1..201</a>
%F A241056 Empirical: a(n) = 9*a(n-2) +12*a(n-3) -36*a(n-4) -94*a(n-5) +42*a(n-6) +366*a(n-7) +182*a(n-8) -847*a(n-9) -1102*a(n-10) +1053*a(n-11) +3109*a(n-12) +196*a(n-13) -5605*a(n-14) -4198*a(n-15) +6248*a(n-16) +11838*a(n-17) -1164*a(n-18) -20204*a(n-19) -9948*a(n-20) +22399*a(n-21) +20007*a(n-22) -15440*a(n-23) -32138*a(n-24) -3232*a(n-25) +46610*a(n-26) +38214*a(n-27) -37132*a(n-28) -43172*a(n-29) +14617*a(n-30) +32371*a(n-31) +36897*a(n-32) +8088*a(n-33) -123047*a(n-34) -63621*a(n-35) +134896*a(n-36) +125072*a(n-37) -107223*a(n-38) -179919*a(n-39) +66957*a(n-40) +285064*a(n-41) -143540*a(n-42) -368756*a(n-43) +184926*a(n-44) +309921*a(n-45) -290298*a(n-46) -125601*a(n-47) +305292*a(n-48) +136259*a(n-49) -258603*a(n-50) +61327*a(n-51) +159050*a(n-52) -38560*a(n-53) -141448*a(n-54) +129709*a(n-55) +7719*a(n-56) -44123*a(n-57) -7193*a(n-58) +55990*a(n-59) -13845*a(n-60) -8760*a(n-61) +20576*a(n-62) -2742*a(n-63) -2230*a(n-64) -2120*a(n-65) -936*a(n-66) -3164*a(n-67) -680*a(n-68) -848*a(n-70) for n>85
%e A241056 Some solutions for n=4
%e A241056 ..3..3..2..2....3..3..2..3....3..2..3..2....3..2..3..3....3..2..3..2
%e A241056 ..2..1..1..0....2..1..1..0....2..1..1..0....2..1..1..2....2..1..1..0
%e A241056 ..2..1..2..3....3..3..2..2....2..1..3..0....2..0..1..2....2..1..2..0
%K A241056 nonn
%O A241056 1,1
%A A241056 _R. H. Hardin_, Apr 15 2014