

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.


3



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
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OFFSET

1,1


LINKS



FORMULA



EXAMPLE

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 2n1) and row 2n1 = (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)*(2n%2) \\ Note: This refers to rows as defined in EXAMPLE, while A061851_row gives the ndigit terms.  M. F. Hasler, Oct 17 2022


CROSSREFS

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


KEYWORD

base,nonn


AUTHOR



STATUS

approved



