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A213081 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.

%I A213081 #14 May 22 2021 04:30:00
%S A213081 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,
%T A213081 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,
%U A213081 8,11,12,3,3,4,13,2,2,13,4,3,3,12,13,15
%N A213081 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.
%e A213081 Table begins:
%e A213081    1;
%e A213081    2,  2;
%e A213081    3,  0,  3;
%e A213081    4,  3,  3,  4;
%e A213081    5,  7,  0,  7,  5;
%e A213081    6,  2,  7,  7,  2,  6;
%e A213081    7,  4,  5,  0,  5,  4,  7;
%e A213081    8,  3,  1,  5,  5,  1,  3,  8;
%e A213081    9, 11,  2,  4,  0,  4,  2, 11,  9;
%e A213081   10,  2,  9,  6,  4,  4,  6,  9,  2, 10;
%e A213081   11,  8, 11, 15,  2,  0,  2, 15, 11,  8, 11;
%o A213081 (Python)
%o A213081 src = [0]*1024
%o A213081 dst = [0]*1024
%o A213081 for i in range(1,39):
%o A213081     dst[0] = dst[i-1] = i
%o A213081     for j in range(1,i-1):
%o A213081         dst[j] = src[j-1]^src[j]
%o A213081     for j in range(i):
%o A213081         src[j] = dst[j]
%o A213081         print(dst[j], end=',')
%Y A213081 Cf. A007318 - Pascal's triangle read by rows.
%Y A213081 Cf. A051597 - Pascal's triangle, begin and end n-th row with n+1, read by rows.
%Y A213081 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).
%K A213081 nonn,tabl,base
%O A213081 1,2
%A A213081 _Alex Ratushnyak_, Jun 04 2012