|
Search: id:A140820
|
|
|
| A140820 |
|
Triangle read by rows: let 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]]; then t(i,j)=If[Sum[b[i, k]*b[j, k], {k, 0, n}] == 0, 1, 0]. |
|
+0
2
|
|
| 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
(list; table; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Row sums are: {1, 1, 1, 2, 2, 1, 2, 4, 4, 2, 1, 2, 4, 2, 4, 8, 8, ...}.
In this method the information is complete: as it is a symbol representation instead of {0,1}, {-1,1} or {1,2} can be used in the output just as well.
This kind of code is used in minimal coding representations like the binary Gray code.
|
|
FORMULA
|
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]]; t(i,j)=If[Sum[b[i, k]*b[j, k], {k, 0, n}] == 0, 1, 0].
|
|
EXAMPLE
|
{1},
{1, 0},
{1, 0, 0},
{1, 1, 0, 0},
{1, 1, 0, 0, 0},
{1, 0, 0, 0, 0, 0},
{1, 0, 0, 1, 0, 0, 0},
{1, 1, 1, 1, 0, 0, 0, 0},
{1, 1, 1, 1, 0, 0, 0, 0, 0},
{1, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}
|
|
MATHEMATICA
|
Clear[c, b, n, a0, d] 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 = 16; a0 = Table[Table[If[Sum[b[i, k]*b[j, k], {k, 0, n}] == 0, 1, 0], {j, 0, i}], {i, 0, n}]; Flatten[a0]
|
|
CROSSREFS
|
Cf. A131218.
Sequence in context: A055088 A068427 A164057 this_sequence A167501 A147612 A080545
Adjacent sequences: A140817 A140818 A140819 this_sequence A140821 A140822 A140823
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 17 2008
|
|
|
Search completed in 0.002 seconds
|
