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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. 2
0, 1, 101, 101001, 1010010001, 101001000100001, 101001000100001000001, 1010010001000010000010000001, 101001000100001000001000000100000001, 101001000100001000001000000100000001000000001 (list; graph; refs; listen; history; text; internal format)
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

a(n)=10^[(1/2)*n]*Sum{k=1..n}{[(1/10)*sqrt(10)]^k*10^[(-1/2)*k^2]}*10^[(1/2)*n^2], with n>=0 - Paolo P. Lava, Oct 06 2008

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

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Last modified August 13 02:52 EDT 2020. Contains 336441 sequences. (Running on oeis4.)