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A232315 Number of (n+1) X (7+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero.

%I A232315 #10 Jul 23 2025 22:56:13
%S A232315 1784,196698,22161823,2499669158,281959315373,31805180533255,
%T A232315 3587649343841650,404689731634719335,45649328032459819031,
%U A232315 5149281019623345273371,580843052186352251086893
%N A232315 Number of (n+1) X (7+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero.
%C A232315 Column 7 of A232316.
%H A232315 R. H. Hardin, <a href="/A232315/b232315.txt">Table of n, a(n) for n = 1..210</a>
%F A232315 Empirical: a(n) = 141*a(n-1) -3378*a(n-2) +21209*a(n-3) +130164*a(n-4) -1632986*a(n-5) -1334372*a(n-6) +50173398*a(n-7) -17669770*a(n-8) -851814078*a(n-9) +566664547*a(n-10) +8298312643*a(n-11) -6773841647*a(n-12) -41349039011*a(n-13) +57182971805*a(n-14) +100779202558*a(n-15) -263951756782*a(n-16) -31349979351*a(n-17) +610312404926*a(n-18) -356266779364*a(n-19) -574818621993*a(n-20) +533901016004*a(n-21) -116525671276*a(n-22) +147213549964*a(n-23) +588901546623*a(n-24) -685413663937*a(n-25) -479062341184*a(n-26) +407490489945*a(n-27) +182418293712*a(n-28) -49631689847*a(n-29) -20468478023*a(n-30) +616705146*a(n-31) +416198455*a(n-32) +31964045*a(n-33) -141509*a(n-34) -15786*a(n-35) -972*a(n-36) +a(n-37) for n>40.
%e A232315 Some solutions for n=2
%e A232315 ..0..0..0..0..0..0..0..0....0..0..1..0..0..0..0..0....0..0..1..1..0..0..0..0
%e A232315 ..0..0..1..0..0..0..1..1....0..1..1..0..0..1..1..0....0..0..0..0..0..0..0..0
%e A232315 ..0..1..0..0..1..1..1..1....1..0..0..1..1..1..0..0....1..1..1..0..1..1..1..1
%Y A232315 Cf. A232316.
%K A232315 nonn
%O A232315 1,1
%A A232315 _R. H. Hardin_, Nov 22 2013