cp's OEIS Frontend

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.

%I A061852 #19 Oct 23 2022 01:34:48
%S A061852 11,22,111,222,1111,2222,11111,22222,110011,111111,220022,222222,
%T A061852 1100011,1111111,2200022,2222222,11000011,11100111,11111111,22000022,
%U A061852 22200222,22222222,110000011,111000111,111111111,220000022,222000222
%N 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.
%H A061852 Ray Chandler, <a href="/A061852/b061852.txt">Table of n, a(n) for n = 1..10000</a>
%F A061852 a(n) = A008919(n)/99.
%e A061852 From _M. F. Hasler_, Oct 17 2022: (Start)
%e A061852 Written in rows, where each row has terms of given length and given digit set (either no 2 or no 1), the sequence starts:
%e A061852   row | terms
%e A061852 ------+------------------------------------
%e A061852     1 | 11
%e A061852     2 | 22
%e A061852     3 | 111
%e A061852     4 | 222
%e A061852     5 | 1111
%e A061852     6 | 2222
%e A061852     7 | 11111
%e A061852     8 | 22222
%e A061852     9 | 110011, 111111
%e A061852    10 | 220022, 222222
%e A061852 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)
%o A061852 (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
%Y A061852 Cf. A008919.
%Y A061852 Union of A061851 and twice A061851.
%Y A061852 Number of terms with k digits is 2*Fibonacci(floor(k/2)) = 2*A000045(A004526(k)) = A006355(floor(k/2)+1).
%K A061852 base,nonn
%O A061852 1,1
%A A061852 _Henry Bottomley_, May 10 2001