A194271 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194270.

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

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-(n-1)^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(n-1)-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