

A194271


Number of toothpicks or Dtoothpicks added at nth stage to the structure of A194270.


19



0, 1, 4, 8, 16, 22, 24, 22, 40, 40, 32, 32, 56, 74, 96, 50, 88, 72, 32, 48, 72, 104, 128, 112, 144, 144, 152, 96, 152, 178, 240, 122, 184, 136, 32, 48, 72, 108, 144, 144, 184, 188, 200, 176, 272, 274, 416, 250, 288, 272, 216, 144, 208, 292, 384, 332, 376
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OFFSET

0,3


COMMENTS

Essentially the first differences of A194270.


LINKS

Table of n, a(n) for n=0..56.
David Applegate, The movie version
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences


FORMULA

a(n) = n^2(n1)^2*(1(1)^n)/8, if 0 <= n <=4.
Let b(n) = A194441(n), let c(n) = A194443(n), let d(n) = A010694(n), then:
Conjecture: a(n) = 4*(b(n1)d(n)) + 2*(c(n)d(n+1)) + 2*(c(n+2)d(n+1)) + 8, if n >= 3.
Conjecture: a(2^k+2) = 32, if k >= 3.


EXAMPLE

Written as a triangle:
0,
1,
4,
8,
16,22,
24,22,40,40,
32,32,56,74,96,50,88,72,
32,48,72,104,128,112,144,144,152,96,152,178,240,122,184,136,
32,48,72,108,144,144,184,188,200,176,272,274,416,250,288,...


CROSSREFS

Cf. A010694, A129370, A139250, A139251, A172311, A182839, A194270, A194441, A194443, A194445.
Sequence in context: A212009 A312809 A312810 * A194701 A220501 A312811
Adjacent sequences: A194268 A194269 A194270 * A194272 A194273 A194274


KEYWORD

nonn


AUTHOR

Omar E. Pol, Aug 23 2011


EXTENSIONS

More terms from Omar E. Pol, Sep 01 2011


STATUS

approved



