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

0,1

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A066957.

Sequence in context: A043940 A220434 A191720 * A250611 A137015 A260903

Adjacent sequences: A066953 A066954 A066955 * A066957 A066958 A066959

Keyword

nice,nonn,base

Author

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

Status

approved