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