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A213081
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Exclusive-or based Pascal triangle, read by rows: T(n,1)=T(n,n)=n and T(n,k) = T(n-1,k-1) XOR T(n-1,k), where XOR is the bitwise exclusive-or operator.
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0
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1, 2, 2, 3, 0, 3, 4, 3, 3, 4, 5, 7, 0, 7, 5, 6, 2, 7, 7, 2, 6, 7, 4, 5, 0, 5, 4, 7, 8, 3, 1, 5, 5, 1, 3, 8, 9, 11, 2, 4, 0, 4, 2, 11, 9, 10, 2, 9, 6, 4, 4, 6, 9, 2, 10, 11, 8, 11, 15, 2, 0, 2, 15, 11, 8, 11, 12, 3, 3, 4, 13, 2, 2, 13, 4, 3, 3, 12, 13, 15
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Table begins:
1;
2, 2;
3, 0, 3;
4, 3, 3, 4;
5, 7, 0, 7, 5;
6, 2, 7, 7, 2, 6;
7, 4, 5, 0, 5, 4, 7;
8, 3, 1, 5, 5, 1, 3, 8;
9, 11, 2, 4, 0, 4, 2, 11, 9;
10, 2, 9, 6, 4, 4, 6, 9, 2, 10;
11, 8, 11, 15, 2, 0, 2, 15, 11, 8, 11;
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PROG
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(Python)
src = [0]*1024
dst = [0]*1024
for i in range(1, 39):
dst[0] = dst[i-1] = i
for j in range(1, i-1):
dst[j] = src[j-1]^src[j]
for j in range(i):
src[j] = dst[j]
print(dst[j], end=', ')
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CROSSREFS
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Cf. A007318 - Pascal's triangle read by rows.
Cf. A051597 - Pascal's triangle, begin and end n-th row with n+1, read by rows.
Cf. A080046 - Multiplicative Pascal triangle, read by rows: T(n,1)=T(n,n)=n and T(n,k) = T(n-1,k-1) * T(n-1,k).
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KEYWORD
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AUTHOR
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STATUS
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approved
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