OFFSET
0,2
COMMENTS
A "sum square" means two consecutive blocks of the same length and same sum.
This is a pure primitive morphic sequence. - N. J. A. Sloane, Jul 14 2018
REFERENCES
Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.
LINKS
David A. Corneth, Table of n, a(n) for n = 0..10000
Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv preprint arXiv:1711.10807, Nov 29 2017
J. Cassaigne, J. D. Currie, L. Schaeffer and J. Shallit, Avoiding Three Consecutive Blocks of the Same Size and Same Sum, arXiv:1106.5204 [cs.DM], 2011.
Michel Rigo, Relations on words, arXiv preprint arXiv:1602.03364 [cs.FL], 2016.
FORMULA
Fixed point of the map 0 -> 03; 1 -> 43; 3 -> 1; 4 -> 01.
EXAMPLE
Start with 0 which maps to 03, then concatenate the image of the second digit, 3, which is 1, so we have 031. Then concatenate the image of the third digit, 1, which is 43. We then have 03143. Etc. - David A. Corneth, Aug 03 2017
MATHEMATICA
Nest[Flatten[# /. {0 -> {0, 3}, 1 -> {4, 3}, 3 -> 1, 4 -> {0, 1}}] &, 0, 9] (* Michael De Vlieger, Aug 03 2017 *)
PROG
(PARI) first(n) = {my(res = [0, 3], i = 2, m = Map(Mat([0, [0, 3]; 1, [4, 3]; 3, [1]; 4, [0, 1]]))); while(#res < n, res = concat(res, mapget(m, res[i])); i++); res} \\ David A. Corneth, Aug 03 2017
CROSSREFS
Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jun 28 2011
STATUS
approved