

A255747


Partial sums of A160552.


10



0, 1, 2, 5, 6, 9, 14, 21, 22, 25, 30, 37, 42, 53, 70, 85, 86, 89, 94, 101, 106, 117, 134, 149, 154, 165, 182, 201, 222, 261, 310, 341, 342, 345, 350, 357, 362, 373, 390, 405, 410, 421, 438, 457, 478, 517, 566, 597, 602, 613, 630, 649, 670, 709, 758, 793, 814, 853, 906, 965, 1046, 1173, 1302, 1365, 1366, 1369, 1374
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OFFSET

0,3


COMMENTS

It appears that the sums of two successive terms give the positive terms of the toothpick sequence A139250.
It appears that the odd terms (a bisection) give A162795.
It appears that a(n) is also the total number of ON cells at stage n+1 in one of the four wedges of twodimensional cellular automaton "Rule 750" using the von Neumann neighborhood (see A169707). Therefore a(n) is also the total number of ON cells at stage n+1 in one of the four quadrants of the NWNESESW version of that cellular automaton.
See also the formula section.
First differs from A169779 at a(11).


LINKS

Ivan Neretin, Table of n, a(n) for n = 0..8191
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.] arXiv:1004.3036
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to cellular automata


FORMULA

It appears that a(n) + a(n1) = A139250(n), n >= 1.
It appears that a(2n1) = A162795(n), n >= 1.
It appears that a(n) = (A169707(n+1)  1)/4.


EXAMPLE

Also, written as an irregular triangle in which the row lengths are the terms of A011782 (the number of compositions of n, n >= 0), the sequence begins:
0;
1;
2, 5;
6, 9, 14, 21;
22, 25, 30, 37, 42, 53, 70, 85;
86, 89, 94,101,106,117,134,149,154,165,182,201,222,261,310,341;
...
It appears that the first column gives 0 together with the terms of A047849, hence the right border gives A002450.
It appears that this triangle only shares with A151920 the positive elements of the columns 1, 2, 4, 8, 16, ... (the powers of 2).


MATHEMATICA

Accumulate[Nest[Join[#, 2 # + Append[Rest@#, 1]] &, {0}, 6]] (* Ivan Neretin, Feb 09 2017 *)


CROSSREFS

Cf. A002450, A011782, A047849, A139250, A151548, A151920, A160552, A162795, A169707, A169779, A246336.
Sequence in context: A224486 A163782 A226793 * A256264 A256249 A169779
Adjacent sequences: A255744 A255745 A255746 * A255748 A255749 A255750


KEYWORD

nonn,changed


AUTHOR

Omar E. Pol, Mar 05 2015


STATUS

approved



