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%I #19 Oct 23 2022 01:34:48
%S 11,22,111,222,1111,2222,11111,22222,110011,111111,220022,222222,
%T 1100011,1111111,2200022,2222222,11000011,11100111,11111111,22000022,
%U 22200222,22222222,110000011,111000111,111111111,220000022,222000222
%N 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 Ray Chandler, <a href="/A061852/b061852.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A008919(n)/99.
%e From _M. F. Hasler_, Oct 17 2022: (Start)
%e 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 row | terms
%e ------+------------------------------------
%e 1 | 11
%e 2 | 22
%e 3 | 111
%e 4 | 222
%e 5 | 1111
%e 6 | 2222
%e 7 | 11111
%e 8 | 22222
%e 9 | 110011, 111111
%e 10 | 220022, 222222
%e 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 (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 Cf. A008919.
%Y Union of A061851 and twice A061851.
%Y Number of terms with k digits is 2*Fibonacci(floor(k/2)) = 2*A000045(A004526(k)) = A006355(floor(k/2)+1).
%K base,nonn
%O 1,1
%A _Henry Bottomley_, May 10 2001
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