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%I #24 Nov 09 2016 09:02:04
%S 1,2,6,24,130,960,9702,134512,2562516,67152240,2422643366,
%T 120395521752,8245524190254,778511553019200,101361018574446630,
%U 18202576574465956224,4509516189662784365688,1541444043912873505870464,727078284287957812245097914
%N Number of n X n X n triangular 0..1 arrays with no 2 X 2 X 2 subblock having three equal elements.
%F a(n) = 2*A007017(n-1) for n>0. - _Alois P. Heinz_, Nov 05 2016
%e Some solutions for n=3:
%e 0 0 0 1 1 1
%e 0 1 1 0 1 1 0 0 1 0 0 1
%e 1 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0
%o (PARI) nextrowcomb(rowarr) = my(k=#rowarr, i=0); while(rowarr[k]==1, rowarr[k]=0; i++; k--); while(rowarr[k]==0 && k > 1, k--); if(rowarr[k]==1, rowarr[k]=0; rowarr[k+1]=1; k=k+2; while(i > 0, rowarr[k]=1; k++; i--), for(x=k, k+i, rowarr[x]=1)); rowarr
%o is_validcombination(toprow, bottomrow) = for(v=1, #toprow, if(toprow[v]==bottomrow[v] && toprow[v]==bottomrow[v+1], return(0))); for(w=2, #toprow, if(toprow[w-1]==bottomrow[w] && toprow[w]==bottomrow[w], return(0))); return(1)
%o terms(n) = my(toprows=[[0], [1]], bottomrow=[0, 0], validrows=[]); while(1, for(k=1, #toprows, if(is_validcombination(toprows[k], bottomrow), validrows=concat(validrows, [bottomrow]))); if(vecmin(bottomrow)==1, bottomrow=vector(#bottomrow+1); print1(#validrows, ", "); toprows=validrows; validrows=[], bottomrow=nextrowcomb(bottomrow)); if(#bottomrow==n+2, break))
%o terms(5) \\ print initial five terms
%Y Cf. A007017, A271069, A271333, A271400.
%K nonn
%O 0,2
%A _Felix Fröhlich_, Nov 05 2016
%E Thanks to _R. H. Hardin_ and _Charles R Greathouse IV_ for helpful suggestions.
%E a(7)-a(18) from _Alois P. Heinz_, Nov 05 2016
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