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 A185587 Irregular triangle read by rows: row n gives a list of the lengths of the free spaces at the n-th stage in a Rule 18 cellular automaton. 1
 1, 3, 1, 1, 1, 7, 1, 5, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 15, 1, 13, 1, 3, 11, 3, 1, 1, 1, 9, 1, 1, 1, 7, 7, 7, 1, 5, 1, 5, 1, 5, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 31, 1, 29, 1, 3, 27, 3, 1, 1, 1, 25, 1, 1, 1, 7, 23, 7, 1, 5, 1, 21, 1, 5, 1, 3, 3, 3, 19, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 15, 15, 15, 1, 13, 1, 13, 1, 13, 1, 3, 11, 3, 11, 3, 11, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the size of the n^th free space inside the development of a Rule 18 CA (related to logical XOR) on a tape started with a single 1. LINKS Benjamin Heiland, Table of n, a(n) for n = 1..154474 EXAMPLE Cellular automaton defined by Rule 18 (with sizes in blank space): (x is a 1 in the automaton, the numbers are the sizes of white spaces)                 x          ->                x1x         ->1               x 3 x        ->3              x1x1x1x       ->1,1,1             x   7   x      ->7            x1x  5  x1x     ->1,5,1           x 3 x 3 x 3 x    ->3,3,3          x1x1x1x1x1x1x1x   ->1,1,1,1,1,1,1 and so on. PROG (C) #include #include int main(){ int inumgen;                   //number of generations int *iacurrentgen;             //current generation int *ialastgen;                //last genereation (to calculate currentgen) int i=0;                       //loop counter int j=0;                       //another loop counter int nullcount=0;               //used to determinate whitespace size int a;                         //a for XOR to get new value int b;                         //b for XOR to get new value iacurrentgen=(int*)calloc(1, sizeof(int)); ialastgen=(int*)calloc(1, sizeof(int)); ialastgen[0]=1; printf("Calculating A185587\n"); printf("please enter number of generations\n"); printf("note that the number of sequence elements per Generation is fluctuating.\n"); scanf("%d", &inumgen); i++;                           //we start at generation1 , not at offset. while(i<=inumgen){   iacurrentgen=(int*)realloc(iacurrentgen, ((i*2+1)*sizeof(int)));   while(j<(i*2+1)){    if((j-2)<0)     a=0;    else     a=ialastgen[j-2];    if(j>((i-1)*2))     b=0;    else     b=ialastgen[j];    iacurrentgen[j]=(a||b)&&!(a&&b);      //(a||b)&&!(a&&b)=aXORb    j++;   }   j=0;   ialastgen=(int*)realloc(ialastgen, ((i*2+1)*sizeof(int)));   while(j<=i*2){    ialastgen[j]=iacurrentgen[j];    if(iacurrentgen[j]==1){     if(nullcount!=0){      printf("%d, ", nullcount);      nullcount=0;     }    }    if(iacurrentgen[j]==0){     nullcount++; }    j++;   }   j=0;   printf("\n");   i++; } } CROSSREFS Cf. A070886 (Rule 90 = Rule 18, starting with 1). Sequence in context: A140670 A293682 A276651 * A068845 A324910 A257100 Adjacent sequences:  A185584 A185585 A185586 * A185588 A185589 A185590 KEYWORD nonn,tabf AUTHOR Benjamin Heiland, Feb 04 2011 STATUS approved

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Last modified July 25 12:56 EDT 2021. Contains 346290 sequences. (Running on oeis4.)