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a(n) = A182841(n+2)/2.
2

%I #43 Feb 24 2021 02:48:19

%S 2,4,7,8,7,12,19,16,7,12,23,32,27,28,43,32,7,12,23,32,31,40,63,72,43,

%T 28,55,84,79,72,99,64,7,12,23,32,31,40,63,72,47,40,71,112,119,112,143,

%U 152,75,28,55,84,91,108,163,204,151,88,131,204,207,180,219,128

%N a(n) = A182841(n+2)/2.

%H Olaf Voß, <a href="/A182842/b182842.txt">Table of n, a(n) for n = 0..998</a>

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

%H 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 Olaf Voß, <a href="/wiki/Toothpick_structures_on_hexagonal_net">Toothpick structures on hexagonal net</a>

%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>

%e From _Omar E. Pol_, Nov 01 2014: (Start)

%e When written as an irregular triangle with row lengths A011782:

%e 2;

%e 4;

%e 7, 8;

%e 7, 12, 19, 16;

%e 7, 12, 23, 32, 27, 28, 43, 32;

%e 7, 12, 23, 32, 31, 40, 63, 72, 43, 28, 55, 84, 79, 72, 99, 64;

%e 7, 12, 23, 32, 31, 40, 63, 72, 47, 40, 71, 112, 119, 112, 143, 152, 75, 28, 55, 84, 91, 108, 163, 204, 151, 88, 131, 204, 207, 180, 219, 128;

%e The right border gives the even powers of 2, at least up a(2^9-1).

%e (End)

%Y Cf. A139250, A139251, A151724, A182633, A182840, A182841.

%K nonn,tabf

%O 0,1

%A _Omar E. Pol_, Dec 11 2010

%E More terms from _Olaf Voß_, Dec 24 2010

%E Wiki link added by _Olaf Voß_, Jan 14 2011