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

0,3

Links

Table of n, a(n) for n=0..9.

Formula

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

Example

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)

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}]

Prog

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

Crossrefs

Cf. A000217, A076131.

Sequence in context: A261881 A262633 A261966 * A180053 A138721 A068659

Adjacent sequences: A076124 A076125 A076126 * A076128 A076129 A076130

Keyword

easy,nonn,base

Author

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

Extensions

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

Status

approved