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A143214
Gray code applied to Pascal's triangle: T(n,k) = GrayCode(binomial(n, k)).
5
1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 6, 5, 6, 1, 1, 7, 15, 15, 7, 1, 1, 5, 8, 30, 8, 5, 1, 1, 4, 31, 50, 50, 31, 4, 1, 1, 12, 18, 36, 101, 36, 18, 12, 1, 1, 13, 54, 126, 65, 65, 126, 54, 13, 1, 1, 15, 59, 68, 187, 130, 187, 68, 59, 15, 1
OFFSET
1,5
LINKS
Eric Weisstein, Gray Code, MathWorld.
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 3, 1;
1, 2, 2, 1;
1, 6, 5, 6, 1;
1, 7, 15, 15, 7, 1;
1, 5, 8, 30, 8, 5, 1;
1, 4, 31, 50, 50, 31, 4, 1;
1, 12, 18, 36, 101, 36, 18, 12, 1;
1, 13, 54, 126, 65, 65, 126, 54, 13, 1;
1, 15, 59, 68, 187, 130, 187, 68, 59, 15, 1;
MATHEMATICA
GrayCode[n_, k_]:= FromDigits[BitXor@@@Partition[Prepend[IntegerDigits[n, 2, k], 0], 2, 1], 2];
A143214[n_, k_]:= GrayCode[Binomial[n-1, k-1], 10];
Table[A143214[n, k], {n, 12}, {k, n}]//Flatten
CROSSREFS
Cf. A143213.
Sequence in context: A338878 A073166 A050169 * A300380 A300682 A300605
KEYWORD
nonn,tabl
AUTHOR
EXTENSIONS
Edited by Michel Marcus and Joerg Arndt, Apr 22 2013
Edited by G. C. Greubel, Aug 27 2024
STATUS
approved