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

0,3

Comments

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

Links

Table of n, a(n) for n=0..14.

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)

Example

   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.

Sequence in context: A107428 A086379 A096460 * A084353 A084979 A049914

Adjacent sequences: A322048 A322049 A322050 * A322052 A322053 A322054

Keyword

nonn

Author

Hugo Pfoertner, Dec 16 2018

Extensions

Edited by M. F. Hasler, Dec 18 2018

Status

approved