A131217 Triangular sequence of a Gray code type made from Pascal's triangle modulo 2 as b(n,m)=Mod[binomial[n,m],2]:A047999: a(n,m)=Mod[b(n,m)+b(n,m+1),2].

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1

Offset

1,1

Comments

An XOR of the sequence terms of A047999 is the algorithm.

Links

Table of n, a(n) for n=1..66.

Formula

b(n,m)=Mod[binomial[n,m],2]: a(n,m)=Mod[b(n,m)+b(n,m+1),2]

Example

{1},
{1, 1},
{1, 1, 1},
{1, 1, 1, 1},
{1, 1, 0, 0, 1},
{1, 1, 0, 0, 1, 1},
{1, 1, 1, 0, 1, 0, 1},
{1, 1, 1, 1, 1, 1, 1, 1},
{1, 1, 0, 0, 0, 0, 0, 0, 1},
{1, 1, 0, 0, 0, 0, 0, 0, 1, 1},
{1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1}

Mathematica

a = Table[Table[Mod[Binomial[n, m], 2], {m, 0, 10}], {n, 0, 10}]; b = Table[Table[If[m <= n && m > 1, Mod[a[[n, m]] + a[[n, m + 1]], 2], 1], {m, 0, n}], {n, 0, 10}]; Flatten[b]

Crossrefs

Cf. A047999, A122944.

Sequence in context: A242902 A196368 A178788 * A105567 A114213 A108358

Adjacent sequences: A131214 A131215 A131216 * A131218 A131219 A131220

Keyword

nonn,uned,tabl

Author

Roger L. Bagula, Sep 27 2007

Status

approved