%I #7 Nov 03 2022 21:49:39
%S 572,1013,1758,3162,6598,13038,24852,51396,102832,196692,406087,
%T 815173,1564506,3229898,6492686,12499511,25777034,51870487,100142925,
%U 206228256,415426219,804167670,1653389401,3334113495,6470363703,13279927241
%N Number of (1+2) X (n+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 3 4 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 3 4 6 or 7.
%C Row 1 of A252640.
%H R. H. Hardin, <a href="/A252641/b252641.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 54*a(n-3) -1300*a(n-6) +a(n-7) +a(n-8) +18442*a(n-9) -46*a(n-10) -48*a(n-11) -171869*a(n-12) +939*a(n-13) +1007*a(n-14) +1112232*a(n-15) -11261*a(n-16) -12125*a(n-17) -5161835*a(n-18) +88673*a(n-19) +92394*a(n-20) +17537697*a(n-21) -486813*a(n-22) -461456*a(n-23) -44251113*a(n-24) +1941080*a(n-25) +1492371*a(n-26) +83816227*a(n-27) -5824359*a(n-28) -2806042*a(n-29) -120301341*a(n-30) +13608098*a(n-31) +1230822*a(n-32) +132500058*a(n-33) -25409661*a(n-34) +8866119*a(n-35) -115158185*a(n-36) +38073643*a(n-37) -28401518*a(n-38) +84586799*a(n-39) -44658830*a(n-40) +46554872*a(n-41) -59077105*a(n-42) +39166599*a(n-43) -48767596*a(n-44) +41880073*a(n-45) -24271783*a(n-46) +33857442*a(n-47) -27389506*a(n-48) +9919627*a(n-49) -15168789*a(n-50) +13979868*a(n-51) -2423220*a(n-52) +4029102*a(n-53) -4453677*a(n-54) +361068*a(n-55) -512244*a(n-56) +193374*a(n-57) -111429*a(n-58) -17496*a(n-59) +514188*a(n-60) -1998*a(n-61) +23328*a(n-62) -196344*a(n-63) +61236*a(n-64) +23328*a(n-66) -21384*a(n-67) for n>74.
%e Some solutions for n=4
%e ..1..2..1..0..3..1....1..3..3..1..0..3....1..3..0..1..3..0....3..3..1..3..0..0
%e ..3..0..1..2..1..1....0..1..3..0..1..3....1..2..1..1..2..0....2..1..1..2..1..0
%e ..1..0..3..3..1..3....1..1..2..1..0..2....3..0..1..3..3..1....3..1..3..0..1..2
%Y Cf. A252640.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 19 2014