cp's OEIS Frontend

A322051 a(n) is the number of initial terms in the row of length 2^n of A322050 that agree with the limiting sequence A322049.

%I A322051 #28 Dec 29 2018 03:43:37
%S A322051 1,1,2,4,6,11,22,43,86,171,342,683,1366,2731,5462
%N A322051 a(n) is the number of initial terms in the row of length 2^n of A322050 that agree with the limiting sequence A322049.
%C A322051 Seems to be identical to A005578 with the exception of a(3) = 4. - _Omar E. Pol_, Dec 17 2018
%F A322051 Conjecture: For n >= 5, a(n) = 2*a(n-1)-1 if n is odd, 2*a(n-1) if n is even.
%F A322051 Conjectures from _Colin Barker_, Dec 29 2018: (Start)
%F A322051 G.f.: (1 - x - x^2 + x^3 - 2*x^4 - x^5 + 2*x^6) / ((1 - x)*(1 + x)*(1 - 2*x)).
%F A322051 a(n) = (2^n + 2) / 3 for n even and n>3.
%F A322051 a(n) = (2^n + 1) / 3 for n odd and n>3.
%F A322051 a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) for n>6.
%F A322051 (End)
%e A322051    n     i*    a(n)  first non-matching pair    (i* = Index of start in A319018)
%e A322051    0      3     1      5      1
%e A322051    1      5     1      7      5
%e A322051    2      9     2      6      3
%e A322051    3     17     4      8      5
%e A322051    4     33     6     17     15
%e A322051    5     65    11    145    141
%e A322051    6    129    22     73     69
%e A322051    7    257    43    734    726
%e A322051    8    513    86    349    341
%e A322051    9   1025   171   3579   3563
%e A322051   10   2049   342   1696   1680
%e A322051   11   4097   683  17810  17778
%e A322051   12   8193  1366   8394   8362
%e A322051   13  16385  2731  88553  88489
%e A322051   14  32769  5462  41665  41601
%e A322051   ...
%Y A322051 Cf. A319018, A319019, A322049, A322050.
%Y A322051 See also A005578.
%K A322051 nonn
%O A322051 0,3
%A A322051 _Hugo Pfoertner_, Dec 16 2018
%E A322051 Edited by _M. F. Hasler_, Dec 18 2018