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A099897 XOR difference triangle, read by rows, of A099898 (in leftmost column) such that the main diagonal equals A099898 shift left and divided by 4.

%I A099897 #11 Jun 13 2017 22:13:06
%S A099897 1,4,5,20,16,21,84,64,80,69,276,320,256,336,277,1108,1344,1024,1280,
%T A099897 1104,1349,5396,4416,5120,4096,5376,4432,5141,20564,17728,21504,16384,
%U A099897 20480,17664,21584,16453,65812,86336,70656,81920,65536,86016,70912
%N A099897 XOR difference triangle, read by rows, of A099898 (in leftmost column) such that the main diagonal equals A099898 shift left and divided by 4.
%C A099897 Central terms of rows equal powers of 4: T(n,[n/2]) = 4^n for n>=0. The leftmost column is A099898. The diagonal forms A099899 and equals the XOR BINOMIAL transform of A099898. See A099884 for the definitions of XOR difference triangle and the XOR BINOMIAL transform.
%F A099897 T(n, [n/2]) = 4^n. T(n+1, 0) = 4*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 A099897 Rows begin:
%e A099897 [_1],
%e A099897 [_4,5],
%e A099897 [20,_16,21],
%e A099897 [84,_64,80,69],
%e A099897 [276,320,_256,336,277],
%e A099897 [1108,1344,_1024,1280,1104,1349],
%e A099897 [5396,4416,5120,_4096,5376,4432,5141],
%e A099897 [20564,17728,21504,_16384,20480,17664,21584,16453],
%e A099897 [65812,86336,70656,81920,_65536,86016,70912,82256,65813],...
%e A099897 notice that the column terms equal 4 times the diagonal (with offset), and that the central terms in the rows form the powers of 4.
%o A099897 (PARI) T(n,k)=if(n<k || k<0,0,if(k==0,if(n==0,1,4*T(n-1,n-1)), bitxor(T(n,k-1),T(n-1,k-1)));)
%Y A099897 Cf. A099884, A099898, A099899, A099900.
%K A099897 nonn,tabl
%O A099897 0,2
%A A099897 _Paul D. Hanna_, Oct 30 2004