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

Author

Henry Bottomley, May 10 2001

Keywords

• base
• nonn

Examples

			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)
		

Links

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

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).

Programs

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

Formula

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