A031265 a(n)=(# 1's)-(# 0's) in first n terms of A031253.
1, 1, 2, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 4, 3, 4, 3, 3, 4, 3, 3, 4, 5, 6, 7, 8, 8, 9, 9, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 13, 13, 13, 14, 14, 13, 14, 14, 14, 15, 15, 15, 15, 14, 15, 15, 14, 14, 14, 15, 14, 14, 15, 15, 15, 16
Offset: 1
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Mathematica
Accumulate[Flatten[Table[IntegerDigits[2n-1,5]/.{0->-1,2->0,3->0,4->0},{n,60}]]] (* Harvey P. Dale, Jan 14 2024 *)