A252162 - OEIS

A252162

Number of (n+2) X (3+2) 0..3 arrays with every 3 X 3 subblock row and column sum equal to 2 3 4 6 or 7 and every 3 X 3 diagonal and antidiagonal sum not equal to 2 3 4 6 or 7.

%I #6 Jun 26 2022 05:23:54

%S 5025,1574,2264,3925,9178,20753,46233,114986,269977,610667,1539618,

%T 3633301,8318037,20933250,49798431,114497817,288734750,688389415,

%U 1593171011,4011260914,9601050751,22286514907,56129462418,134544121435

%N Number of (n+2) X (3+2) 0..3 arrays with every 3 X 3 subblock row and column sum equal to 2 3 4 6 or 7 and every 3 X 3 diagonal and antidiagonal sum not equal to 2 3 4 6 or 7.

%C Column 3 of A252167.

%H R. H. Hardin, <a href="/A252162/b252162.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-2) +26*a(n-3) +9*a(n-4) -52*a(n-5) -177*a(n-6) -234*a(n-7) +356*a(n-8) +142*a(n-9) +1633*a(n-10) -336*a(n-11) -130*a(n-12) -2318*a(n-13) +622*a(n-14) +463*a(n-15) +8410*a(n-16) -1418*a(n-17) +1511*a(n-18) -14007*a(n-19) -1314*a(n-20) -3452*a(n-21) +20561*a(n-22) +4010*a(n-23) +4977*a(n-24) -26812*a(n-25) -6144*a(n-26) -7783*a(n-27) +31407*a(n-28) +10894*a(n-29) +10540*a(n-30) -23393*a(n-31) -15794*a(n-32) -6244*a(n-33) +10860*a(n-34) +9366*a(n-35) +128*a(n-36) -6244*a(n-37) -192*a(n-38) +128*a(n-40) for n>45.

%e Some solutions for n=4

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

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

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

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

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

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

%Y Cf. A252167.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 14 2014