

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
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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. 56. [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. 56. [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 7 generations of A161644 and A295560 (edgetoedge version)
N. J. A. Sloane, Illustration of first 11 generations of A161644 and A295560 (vertextovertex 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, zeros1) else if (zeros==0) r=BVal(ones+1, ones+1) else r=BVal(ones+2, ones+zeros)
else
if (len==zeros+1) r=AVal(zeros2) else r=AVal(ones+zeros1)
and
AVal(k)=6*(2^(k+1)1)
BVal(k, kk)=3*2^k + sum(j=0,kk1, 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, kk1, 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, len2, ones+=bittest(n, j));
if (bittest(n, 0)==1,
if (len==zeros+2, r=BVal(1, zeros1), if (zeros==0, r=BVal(ones+1, ones+1), r=BVal(ones+2, ones+zeros))),
if (len==zeros+1, r=AVal(zeros2), r=AVal(ones+zeros1)));
r; }
vector(200, i, A295559(i1))
\\ 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



