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are g(2010), g(2011) divisible by 11? sum of n-digits form digits 0,1,2,3 such

Source: 2011 Belarus TST 5.1

November 7, 2020
number theoryDigitsSumdivisible

Problem Statement

Let g(n)g(n) be the number of all nn-digit natural numbers each consisting only of digits 0,1,2,30,1,2,3 (but not nessesarily all of them) such that the sum of no two neighbouring digits equals 22. Determine whether g(2010)g(2010) and g(2011)g(2011) are divisible by 1111.
I.Kozlov
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