A277211 Number of n X n X n triangular 0..1 arrays with no 2 X 2 X 2 subblock having three equal elements.

1, 2, 6, 24, 130, 960, 9702, 134512, 2562516, 67152240, 2422643366, 120395521752, 8245524190254, 778511553019200, 101361018574446630, 18202576574465956224, 4509516189662784365688, 1541444043912873505870464, 727078284287957812245097914

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = 2*A007017(n-1) for n>0. - Alois P. Heinz, Nov 05 2016

Example

Some solutions for n=3:
     0      0      0      1      1      1
    0 1    1 0    1 1    0 0    1 0    0 1
   1 0 0  0 1 1  1 0 1  0 1 1  0 0 1  1 1 0

Prog

(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
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)
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))
terms(5) \\ print initial five terms

Crossrefs

Cf. A007017, A271069, A271333, A271400.

Sequence in context: A191343 A368761 A052862 * A374153 A370017 A343482

Adjacent sequences: A277208 A277209 A277210 * A277212 A277213 A277214

Keyword

nonn

Author

Felix Fröhlich, Nov 05 2016

Extensions

Thanks to R. H. Hardin and Charles R Greathouse IV for helpful suggestions.

a(7)-a(18) from Alois P. Heinz, Nov 05 2016

Status

approved