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 A295559 Same as A161645 except that triangles must always grow outwards. 5
 0, 1, 3, 6, 6, 6, 12, 18, 12, 6, 12, 18, 18, 18, 30, 42, 24, 6, 12, 18, 18, 18, 30, 42, 30, 18, 30, 42, 42, 42, 66, 90, 48, 6, 12, 18, 18, 18, 30, 42, 30, 18, 30, 42, 42, 42, 66, 90, 54, 18, 30, 42, 42, 42, 66, 90, 66, 42, 66, 90, 90, 90, 138, 186, 96, 6, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Note that Reed's version has errors (see A295558). REFERENCES R. Reed, The Lemming Simulation Problem, Mathematics in School, 3 (#6, Nov. 1974), front cover and pp. 5-6. [Describes the dual structure where new triangles are joined at vertices rather than edges.] LINKS Lars Blomberg, Table of n, a(n) for n = 0..10000 R. Reed, The Lemming Simulation Problem, Mathematics in School, 3 (#6, Nov. 1974), front cover and pp. 5-6. [Scanned photocopy of pages 5, 6 only, with annotations by R. K. Guy and N. J. A. Sloane] N. J. A. Sloane, Illustration of first 11 generations of A161644 and A295560 (vertex-to-vertex version) [Include the 6 cells marked x to get A161644(11), exclude them to get A295560(11).] N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS FORMULA From Lars Blomberg, Dec 20 2017: (Start) Empirically (correct to 3*10^6 terms): Convert n+1 to binary and view it as 1a1b or 1a1b1, where a is zero or more digits, let "ones" be the number of 1's in a, and b is zero or more 0's, let "zeros" be the number of 0's. Let "len" be the total number of binary digits. Then r=A295559(n) is determined by ones, zeros, len, and the parity of n+1, as follows: if (n==0,1,2) r=0,1,3 else if (n+1 is odd)     if (len==zeros+2) r=BVal(1, zeros-1) else if (zeros==0) r=BVal(ones+1, ones+1) else r=BVal(ones+2, ones+zeros) else     if (len==zeros+1) r=AVal(zeros-2) else r=AVal(ones+zeros-1) and AVal(k)=6*(2^(k+1)-1) BVal(k, kk)=3*2^k + sum(j=0,kk-1, 6 * 2^j) (End) PROG (PARI) \\ Empirically discovered algorithm. AVal(k)=6*(2^(k+1)-1) BVal(k, kk)={ local v; v = 3 * 2^k; for (j=0, kk-1, v += 6 * 2^j); v} A295559(n)={ local (len, zeros, ones, r); if(n==0, return(0)); if(n==1, return(1)); if(n==2, return(3)); n++; len=length(binary(n)); zeros=ones=0; i=bittest(n, 0);  \\ Skip trailing 1 while(bittest(n, i)==0, zeros++; i++); for(j=i+1, len-2, ones+=bittest(n, j)); if (bittest(n, 0)==1, if (len==zeros+2, r=BVal(1, zeros-1), if (zeros==0, r=BVal(ones+1, ones+1), r=BVal(ones+2, ones+zeros))), if (len==zeros+1, r=AVal(zeros-2), r=AVal(ones+zeros-1))); r; } vector(200, i, A295559(i-1)) \\ Lars Blomberg, Dec 20 2017 CROSSREFS Cf. A161644, A161645, A295560. Sequence in context: A155067 A094011 A295558 * A161645 A081289 A160504 Adjacent sequences:  A295556 A295557 A295558 * A295560 A295561 A295562 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 27 2017 EXTENSIONS Terms a(18) and beyond from Lars Blomberg, Dec 20 2017 STATUS approved

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Last modified August 2 08:47 EDT 2021. Contains 346422 sequences. (Running on oeis4.)