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

%I A194271 #35 Nov 23 2019 04:05:40
%S A194271 0,1,4,8,16,22,24,22,40,40,32,32,56,74,96,50,88,72,32,48,72,104,128,
%T A194271 112,144,144,152,96,152,178,240,122,184,136,32,48,72,108,144,144,184,
%U A194271 188,200,176,272,274,416,250,288,272,216,144,208,292,384,332,376
%N A194271 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194270.
%C A194271 Essentially the first differences of A194270.
%H A194271 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>
%H A194271 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H A194271 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F A194271 a(n) = n^2-(n-1)^2*(1-(-1)^n)/8, if 0 <= n <=4.
%F A194271 Let b(n) = A194441(n), let c(n) = A194443(n), let d(n) = A010694(n), then:
%F A194271 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.
%F A194271 Conjecture: a(2^k+2) = 32, if k >= 3.
%e A194271 Written as a triangle:
%e A194271 0,
%e A194271 1,
%e A194271 4,
%e A194271 8,
%e A194271 16,22,
%e A194271 24,22,40,40,
%e A194271 32,32,56,74,96,50,88,72,
%e A194271 32,48,72,104,128,112,144,144,152,96,152,178,240,122,184,136,
%e A194271 32,48,72,108,144,144,184,188,200,176,272,274,416,250,288,...
%Y A194271 Cf. A010694, A129370, A139250, A139251, A172311, A182839, A194270, A194441, A194443, A194445.
%K A194271 nonn
%O A194271 0,3
%A A194271 _Omar E. Pol_, Aug 23 2011
%E A194271 More terms from _Omar E. Pol_, Sep 01 2011