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A203654 1/25 the number of (n+1)X7 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

%I A203654 #7 Jul 22 2025 17:25:20
%S A203654 531441,178019197,71156938905,30292030417413,13192335511091073,
%T A203654 5796397762880763341,2554890395768832271017,1127594169687376371159253,
%U A203654 497870086469175871336506385,219871060492143544799371582749
%N A203654 1/25 the number of (n+1)X7 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.
%C A203654 Column 6 of A203656
%H A203654 R. H. Hardin, <a href="/A203654/b203654.txt">Table of n, a(n) for n = 1..210</a>
%F A203654 Empirical: a(n) = 329*a(n-1) +107668*a(n-2) -25063968*a(n-3) -680298432*a(n-4) +202122434560*a(n-5) +566048790528*a(n-6) -556012878114816*a(n-7) +3504577252474880*a(n-8) +591608256378830848*a(n-9) -6839009506476949504*a(n-10) -239163894638688862208*a(n-11) +3525511542366864932864*a(n-12) +35450315597944711020544*a(n-13) -664062013074729355706368*a(n-14) -1530140375300205031981056*a(n-15) +50183396342386988796608512*a(n-16) -17094562720050709209808896*a(n-17) -1622789056358547469740539904*a(n-18) +2031702560273665184466206720*a(n-19) +21489007078579909036995510272*a(n-20) -30394434853378035268349591552*a(n-21) -101547952483445807369349496832*a(n-22) +114461568017537120233548939264*a(n-23) +177927593591172462047265816576*a(n-24) -114513709337590944825725681664*a(n-25) -72325116345546289517124648960*a(n-26) +34013569597018368539319336960*a(n-27) -3061173118029560521791897600*a(n-28)
%e A203654 Some solutions for n=4
%e A203654 ..4..2..4..2..4..1..1....0..4..4..2..4..3..0....0..0..0..2..1..1..2
%e A203654 ..1..4..4..4..2..4..1....3..0..4..4..4..4..3....1..0..3..0..2..1..1
%e A203654 ..0..1..4..3..4..2..4....3..3..0..4..0..4..4....3..1..0..0..0..2..1
%e A203654 ..4..0..1..4..0..4..4....0..3..3..0..2..0..4....1..4..1..0..0..0..2
%e A203654 ..2..4..0..1..4..1..4....0..0..3..3..0..4..3....4..2..4..1..0..3..0
%K A203654 nonn
%O A203654 1,1
%A A203654 _R. H. Hardin_ Jan 04 2012