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

Author

Omar E. Pol, Aug 23 2011

Keywords

• nonn

Comments

Essentially the first differences of A194270.

Examples

			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,...
		

Links

• 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

Crossrefs

Cf. A010694, A129370, A139250, A139251, A172311, A182839, A194270, A194441, A194443, A194445.

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.

Extensions

More terms from Omar E. Pol, Sep 01 2011