A066956 a(n) is the number of ways of placing '+' and '-' among the digits 123456789 so that the result of the expression is n, '-' before 1 not allowed.

11, 26, 11, 18, 8, 21, 12, 17, 8, 22, 12, 21, 11, 16, 15, 20, 8, 17, 11, 20, 15, 16, 11, 23, 18, 13, 14, 21, 15, 19, 17, 14, 19, 19, 7, 14, 19, 19, 17, 18, 16, 17, 18, 10, 15, 26, 18, 15, 16, 12, 17, 19, 9, 17, 21, 16, 13, 14, 16, 17, 17, 11, 13, 22, 14, 13, 15, 15, 15, 17, 7

Offset: 0

Author

Miklos SZABO (mike(AT)ludens.elte.hu), Feb 01 2002

Keywords

• nice
• nonn
• base

Comments

a(n) = 0 for all but finitely many n. In particular, a(n) = 0 for n > 123456789. - Charles R Greathouse IV, Aug 20 2012

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..34668

Crossrefs

Cf. A066957.

Programs

Python

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