A061852 Digital representation of m contains only either 1's or 2's (but not both 1's and 2's) and 0's, is palindromic and contains no singleton 2's, 1's or 0's.

11, 22, 111, 222, 1111, 2222, 11111, 22222, 110011, 111111, 220022, 222222, 1100011, 1111111, 2200022, 2222222, 11000011, 11100111, 11111111, 22000022, 22200222, 22222222, 110000011, 111000111, 111111111, 220000022, 222000222

Offset

1,1

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Formula

a(n) = A008919(n)/99.

Example

From M. F. Hasler, Oct 17 2022: (Start)
Written in rows, where each row has terms of given length and given digit set (either no 2 or no 1), the sequence starts:
  row | terms
------+------------------------------------
    1 | 11
    2 | 22
    3 | 111
    4 | 222
    5 | 1111
    6 | 2222
    7 | 11111
    8 | 22222
    9 | 110011, 111111
   10 | 220022, 222222
Then for any n >= 1, row 2n = 2*(row 2n-1) and row 2n-1 = (terms in A061851 with n+1 digits), and the number of terms in row n is Fibonacci(ceiling(n/4)) = A000045(A002265(n+3)), and their length (number of digits) is ceiling(n/2)+1 = floor((n+3)/2). (End)

Prog

(PARI) A061852_row(n)=A061851_row(n\/2+1)*(2-n%2) \\ Note: This refers to rows as defined in EXAMPLE, while A061851_row gives the n-digit terms. - M. F. Hasler, Oct 17 2022

Crossrefs

Cf. A008919.

Union of A061851 and twice A061851.

Number of terms with k digits is 2*Fibonacci(floor(k/2)) = 2*A000045(A004526(k)) = A006355(floor(k/2)+1).

Sequence in context: A034708 A091784 A213972 * A083511 A067894 A094620

Adjacent sequences: A061849 A061850 A061851 * A061853 A061854 A061855

Keyword

base,nonn

Author

Henry Bottomley, May 10 2001

Status

approved