cp's OEIS Frontend

A367555 Number of zeros (or ones) in each row of the iterates of the Christmas tree pattern map (A367508).

%I A367555 #21 Nov 29 2023 07:46:04
%S A367555 1,1,3,3,3,6,2,6,2,6,6,10,5,5,10,5,5,10,5,10,10,15,3,9,3,9,9,15,3,9,3,
%T A367555 9,9,15,3,9,9,15,9,15,15,21,7,7,14,7,7,14,7,14,14,21,7,7,14,7,7,14,7,
%U A367555 14,14,21,7,7,14,7,14,14,21,7,14,14,21,14,21,21,28
%N A367555 Number of zeros (or ones) in each row of the iterates of the Christmas tree pattern map (A367508).
%C A367555 See A367508 for the description of the Christmas tree patterns, references and links.
%H A367555 Paolo Xausa, <a href="/A367555/b367555.txt">Table of n, a(n) for n = 1..13494</a> (first 15 orders).
%e A367555 The following diagram shows the first 4 tree pattern orders, along with the corresponding number of zeros = number of ones.
%e A367555 .
%e A367555 Order 1:                        |
%e A367555               0  1              |   1
%e A367555                                 |
%e A367555 Order 2:                        |
%e A367555                10               |   1
%e A367555            00  01  11           |   3
%e A367555                                 |
%e A367555 Order 3:                        |
%e A367555             100  101            |   3
%e A367555             010  110            |   3
%e A367555        000  001  011  111       |   6
%e A367555                                 |
%e A367555 Order 4:                        |
%e A367555               1010              |   2
%e A367555         1000  1001  1011        |   6
%e A367555               1100              |   2
%e A367555         0100  0101  1101        |   6
%e A367555         0010  0110  1110        |   6
%e A367555   0000  0001  0011  0111  1111  |  10
%e A367555 .
%t A367555 With[{imax=9},Map[Total,NestList[Map[Delete[{If[Length[#]>1,Rest[#],Nothing],Join[{First[#]},#+1]},0]&],{{0,1}},imax-1],{2}]] (* Generates terms up to order 9 *)
%o A367555 (Python)
%o A367555 from itertools import islice
%o A367555 from functools import reduce
%o A367555 def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])
%o A367555 def agen():  # generator of terms
%o A367555     R = [["0", "1"]]
%o A367555     while R:
%o A367555         r = R.pop(0)
%o A367555         yield sum(e.count("1") for e in r)
%o A367555         if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))
%o A367555         R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))
%o A367555 print(list(islice(agen(), 77))) # _Michael S. Branicky_, Nov 23 2023
%Y A367555 Cf. A367508, A367562.
%K A367555 nonn,base
%O A367555 1,3
%A A367555 _Paolo Xausa_, Nov 22 2023