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A143213
Triangle T(n,m) read by rows: Gray code of A060187(n, k) (decimal representation), 1 <= k <= n, n >= 1.
2
1, 1, 1, 1, 5, 1, 1, 28, 28, 1, 1, 106, 149, 106, 1, 1, 155, 987, 987, 155, 1, 1, 955, 440, 514, 440, 955, 1, 1, 194, 137, 974, 974, 137, 194, 1, 1, 340, 754, 60, 293, 60, 754, 340, 1, 1, 181, 238, 166, 377, 377, 166, 238, 181, 1, 1, 977, 283, 540, 411, 142, 411, 540, 283, 977, 1
OFFSET
1,5
LINKS
Eric Weisstein, Gray Code, MathWorld.
FORMULA
T(n, n-k) = T(n, k). - G. C. Greubel, Aug 08 2024
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 5, 1;
1, 28, 28, 1;
1, 106, 149, 106, 1;
1, 155, 987, 987, 155, 1;
1, 955, 440, 514, 440, 955, 1;
1, 194, 137, 974, 974, 137, 194, 1;
1, 340, 754, 60, 293, 60, 754, 340, 1;
1, 181, 238, 166, 377, 377, 166, 238, 181, 1;
1, 977, 283, 540, 411, 142, 411, 540, 283, 977, 1;
MATHEMATICA
GrayCode[n_, k_]:= FromDigits[BitXor@@@Partition[Prepend[IntegerDigits[n, 2, k], 0], 2, 1], 2];
A060187[n_, k_]:= Sum[(-1)^(k-j)*Binomial[n, k-j]*(2*j-1)^(n-1), {j, k}];
A143213[n_, k_]:= GrayCode[A060187[n, k], 10];
Table[A143213[n, k], {n, 12}, {k, n}]//Flatten
CROSSREFS
Sequence in context: A176793 A118190 A172342 * A172377 A156587 A058720
KEYWORD
nonn,tabl
AUTHOR
EXTENSIONS
Edited by G. C. Greubel, Aug 27 2024
STATUS
approved