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def T(a, b): return ((a + b)**2 + 3*a + b)//2
for n in range(0, 21): print ([A(k, n - k) for k in range(0, n + 1)] ) # Indranil Ghosh, May 21 2017
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for n in xrangerange(0, 21): print [A(k, n - k) for k in xrangerange(0, n + 1)] # Indranil Ghosh, May 21 2017
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T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitXor[n, k], k]; Table[A[k, n - k ], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *)
(Python)
def T(a, b): return ((a + b)**2 + 3*a + b)/2
def A(n, k): return T(n^k, k)
for n in xrange(0, 21): print [A(k, n - k) for k in xrange(0, n + 1)] # Indranil Ghosh, May 21 2017
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