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, 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
Offset: 1
Examples
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.
Links
- Benjamin Heiland, Table of n, a(n) for n = 1..154474
Crossrefs
Cf. A070886 (Rule 90 = Rule 18, starting with 1).
Programs
-
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++; } }
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