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A099900 XOR difference triangle, read by rows, of A099901 (in leftmost column) such that the main diagonal equals A099901 shift left and divided by 2.

%I A099900 #11 Jun 13 2017 22:13:08
%S A099900 1,2,3,6,4,7,14,8,12,11,22,24,16,28,23,46,56,32,48,44,59,118,88,96,64,
%T A099900 112,92,103,206,184,224,128,192,176,236,139,278,472,352,384,256,448,
%U A099900 368,412,279,558,824,736,896,512,768,704,944,556,827,1654,1112,1888,1408
%N A099900 XOR difference triangle, read by rows, of A099901 (in leftmost column) such that the main diagonal equals A099901 shift left and divided by 2.
%C A099900 Central terms of rows equal powers of 2: T(n,[n/2]) = 2^n for n>=0. The leftmost column is A099901. The diagonal forms A099902 and equals the XOR BINOMIAL transform of A099901.
%F A099900 T(n, [n/2]) = 2^n. T(n+1, 0) = 2*T(n, n) (n>=0); T(0, 0)=1; T(n, k) = T(n, k-1) XOR T(n-1, k-1) for n>k>0. T(n, k) = SumXOR_{i=0..k} (C(k, i)mod 2)*T(n-i, 0), where SumXOR is the analog of summation under the binary XOR operation and C(k, i)mod 2 = A047999(k, i).
%e A099900 Rows begin:
%e A099900 [_1],
%e A099900 [_2,3],
%e A099900 [6,_4,7],
%e A099900 [14,_8,12,11],
%e A099900 [22,24,_16,28,23],
%e A099900 [46,56,_32,48,44,59],
%e A099900 [118,88,96,_64,112,92,103],
%e A099900 [206,184,224,_128,192,176,236,139],
%e A099900 [278,472,352,384,_256,448,368,412,279],
%e A099900 [558,824,736,896,_512,768,704,944,556,827],
%e A099900 [1654,1112,1888,1408,1536,_1024,1792,1472,1648,1116,1895],...
%e A099900 notice that the column terms equal twice the diagonal (with offset), and that the central terms in the rows form the powers of 2.
%o A099900 (PARI) T(n,k)=if(n<k || k<0,0,if(k==0,if(n==0,1,2*T(n-1,n-1)), bitxor(T(n,k-1),T(n-1,k-1)));)
%Y A099900 Cf. A099884, A099901, A099902.
%K A099900 eigen,nonn,tabl
%O A099900 0,2
%A A099900 _Paul D. Hanna_, Oct 29 2004