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A241351 Number of n X 3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of 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. 1

%I #6 Jun 26 2022 19:59:55

%S 4,9,19,55,72,124,243,370,695,956,1417,2469,3404,5728,8713,12387,

%T 19273,29598,44909,73642,107481,163546,255220,378761,599088,925233,

%U 1374249,2146719,3251091,4948266,7795540,11712323,17982730,27767716,41826534

%N Number of n X 3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of 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 Column 3 of A241356.

%H R. H. Hardin, <a href="/A241351/b241351.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-5) +4*a(n-6) +5*a(n-8) +2*a(n-9) +16*a(n-11) +3*a(n-13) +6*a(n-14) -10*a(n-15) -22*a(n-16) -2*a(n-17) -13*a(n-18) +26*a(n-19) -18*a(n-20) +18*a(n-21) -49*a(n-22) -2*a(n-23) -21*a(n-24) +18*a(n-25) +22*a(n-26) +61*a(n-27) -62*a(n-28) -13*a(n-29) -102*a(n-30) -32*a(n-31) +71*a(n-32) +43*a(n-33) +30*a(n-34) +53*a(n-35) -34*a(n-36) -204*a(n-37) +137*a(n-38) -22*a(n-39) +80*a(n-40) +108*a(n-41) +118*a(n-42) -242*a(n-43) +150*a(n-44) -100*a(n-45) +49*a(n-46) -3*a(n-47) +176*a(n-48) -162*a(n-49) +87*a(n-50) -118*a(n-51) +40*a(n-52) -89*a(n-53) +74*a(n-54) -11*a(n-55) +4*a(n-56) -65*a(n-57) +62*a(n-58) -91*a(n-59) +20*a(n-60) -22*a(n-61) +38*a(n-62) -20*a(n-63) +21*a(n-64) -19*a(n-65) +7*a(n-66) -5*a(n-67) +2*a(n-68) for n>85.

%e Some solutions for n=4

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

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

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

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

%Y Cf. A241356.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 20 2014

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Last modified March 4 05:23 EST 2024. Contains 370522 sequences. (Running on oeis4.)