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%I #13 Jan 01 2024 11:05:15
%S 0,1,101,101001,1010010001,101001000100001,101001000100001000001,
%T 1010010001000010000010000001,101001000100001000001000000100000001,
%U 101001000100001000001000000100000001000000001
%N n-th term is binary string of length t_n with 1's at positions t_i, where t_n = n-th triangular number.
%F if(n==0), a(0)=0; else a(n)=10^n*a(n-1)+1
%e For example, the first 4 strings are: '1' (length 1, nonzero index 1), '101' (length 3, nonzero indices 1,3), '101001' (length 6, nonzero indices 1,3,6) '1010010001' (length 10, nonzero indices 1,3,6,10)
%t f[n_] := Block[{a = {1}}, Do[a = Join[a, Table[0, {i}], {1}], {i, 1, n}]; FromDigits[a]]; Table[ f[n], {n, 0, 8}]
%o (PARI) a(n)=if(n<1,0,1+a(n-1)*10^n)
%o (PARI) a(n)=subst( Polrev( Vec( sum(k=1, n, x^(k*(k+1)/2)))), x, 10)
%o (MATLAB) function ans=bstn(n) if(n==0), ans=0; else, ans=10^n*bstn(n-1)
%Y Cf. A000217, A076131.
%K easy,nonn,base
%O 0,3
%A Kyle Hunter (hunterk(AT)raytheon.com), Oct 31 2002
%E Edited and extended by _Robert G. Wilson v_, Oct 31 2002
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