A131219 a(n,m) = (binomial(n,m) mod 2)*Gray_Code(n,m).

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Formula

a(n,m) = (binomial(n,m) mod 2)*Gray_Code(n,m).

Example

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

Mathematica

c[i_, k_] := Floor[Mod[i/2^k, 2]];
b[i_, k_] = If[c[i, k] == 0 && c[i, k + 1] == 0, 0, If[c[i, k] == 1 && c[i, k + 1] == 1, 0, 1]];
n = 15
a0 = Table[If[Sum[b[i, k]*b[j, k], {k, 0, n}] == 0, 1, 0], {j, 0, n}, {i, 0, n}];
ListDensityPlot[a0, Mesh -> False];
c = Delete[Table[Reverse[Table[a0[[n, l - n]], {n, 1, l - 1}]], {l, 1, Dimensions[a0][[1]] + 1}], 1];
Flatten[c];
Dimensions[c];
d = Table[Table[Mod[Binomial[n0, m], 2], {m, 0, n0}], {n0, 0, n}]
e = Table[Table[c[[n0, m]]*d[[n0, m]], {m, 1, n0}], {n0, 1, n + 1}]
Flatten[e]

Crossrefs

Cf. A047999.

Sequence in context: A127972 A103451 A103452 * A127970 A158856 A154957

Adjacent sequences: A131216 A131217 A131218 * A131220 A131221 A131222

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Sep 27 2007

Status

approved