A076127 n-th term is binary string of length t_n with 1's at positions t_i, where t_n = n-th triangular number.

0, 1, 101, 101001, 1010010001, 101001000100001, 101001000100001000001, 1010010001000010000010000001, 101001000100001000001000000100000001, 101001000100001000001000000100000001000000001

Offset: 0

Author

Kyle Hunter (hunterk(AT)raytheon.com), Oct 31 2002

Keywords

• easy
• nonn
• base

Examples

			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)
		

Crossrefs

Cf. A000217, A076131.

Programs

MATLAB

function ans=bstn(n) if(n==0), ans=0; else, ans=10^n*bstn(n-1)

Mathematica

f[n_] := Block[{a = {1}}, Do[a = Join[a, Table[0, {i}], {1}], {i, 1, n}]; FromDigits[a]]; Table[ f[n], {n, 0, 8}]

PARI

a(n)=if(n<1,0,1+a(n-1)*10^n)

PARI

a(n)=subst( Polrev( Vec( sum(k=1, n, x^(k*(k+1)/2)))), x, 10)

Formula

if(n==0), a(0)=0; else a(n)=10^n*a(n-1)+1

Extensions

Edited and extended by Robert G. Wilson v, Oct 31 2002