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A277211 Number of n X n X n triangular 0..1 arrays with no 2 X 2 X 2 subblock having three equal elements. 0
1, 2, 6, 24, 130, 960, 9702, 134512, 2562516, 67152240, 2422643366, 120395521752, 8245524190254, 778511553019200, 101361018574446630, 18202576574465956224, 4509516189662784365688, 1541444043912873505870464, 727078284287957812245097914 (list; graph; refs; listen; history; text; internal format)
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: A201158 A191343 A052862 * A216779 A129101 A292907

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

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Last modified February 19 12:48 EST 2018. Contains 299333 sequences. (Running on oeis4.)