This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(4) = 8 because 4 = 12-34-56-7+89 = 12-3-4-5-6-7+8+9 = 12-3+45-67+8+9 = 12-3+4-5+6+7-8-9 = 12-3+4+5-6-7+8-9 = 12+3-4-5+6-7+8-9 = 12+3-4+5-6-7-8+9 = 1+2-34+5+6+7+8+9 and only for these.
from collections import Counter
from itertools import product, zip_longest
def aupton(nn):
digs = list("123456789")
c = Counter(eval("".join(filter(None, sum(zip_longest(digs, ops), ())))) for ops in product(["-", "+", ""], repeat=8))
return [c[k] for k in range(nn+1)]
print(aupton(70)) # Michael S. Branicky, Nov 26 2021
a(1) = 176 = 1 - 2 + 34 + 56 + 78 + 9; a(2) = 191 = 123 + 4 + 56 + 7 - 8 + 9; a(3) = 194 = 1 - 2 + 34 + 5 + 67 + 89; a(4) = 196 = -1 + 2 + 34 + 5 + 67 + 89; a(5) = 209 = 1 + 234 + 56 + 7 - 89; a(6) = 213 = 123 + 4 + 5 - 6 + 78 + 9; a(7) = 215 = 123 + 4 - 5 + 6 + 78 + 9; a(8) = 217 = 123 - 4 + 5 + 6 + 78 + 9; a(9) = 223 = -1 + 23 + 45 + 67 + 89; a(10) = 237 = -123 + 456 - 7 - 89; a(11) = 253 = -1 + 2 + 345 - 6 - 78 - 9; a(12) = 259 = -1 + 234 - 56 - 7 + 89; a(869) = 123456789 = A136602(1715).
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