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.

1, 1, 2, 4, 6, 11, 22, 43, 86, 171, 342, 683, 1366, 2731, 5462

Offset: 0

Author

Hugo Pfoertner, Dec 16 2018

Keywords

• nonn

Comments

Seems to be identical to A005578 with the exception of a(3) = 4. - Omar E. Pol, Dec 17 2018

Examples

			   n     i*    a(n)  first non-matching pair    (i* = Index of start in A319018)
   0      3     1      5      1
   1      5     1      7      5
   2      9     2      6      3
   3     17     4      8      5
   4     33     6     17     15
   5     65    11    145    141
   6    129    22     73     69
   7    257    43    734    726
   8    513    86    349    341
   9   1025   171   3579   3563
  10   2049   342   1696   1680
  11   4097   683  17810  17778
  12   8193  1366   8394   8362
  13  16385  2731  88553  88489
  14  32769  5462  41665  41601
  ...
		

Crossrefs

Cf. A319018, A319019, A322049, A322050.

See also A005578.

Formula

Conjecture: For n >= 5, a(n) = 2*a(n-1)-1 if n is odd, 2*a(n-1) if n is even.

Conjectures from Colin Barker, Dec 29 2018: (Start)

G.f.: (1 - x - x^2 + x^3 - 2*x^4 - x^5 + 2*x^6) / ((1 - x)*(1 + x)*(1 - 2*x)).

a(n) = (2^n + 2) / 3 for n even and n>3.

a(n) = (2^n + 1) / 3 for n odd and n>3.

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) for n>6.

(End)

Extensions

Edited by M. F. Hasler, Dec 18 2018