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A335979
Number of partitions of n into exactly two parts with no decimal carries.
0
0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 7, 9, 12, 14, 17, 19, 22, 24, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 3, 6, 10, 13, 17, 20, 24, 27, 31, 34, 3, 7, 11, 15, 19, 23
OFFSET
0,5
COMMENTS
a(m) = a(n) if m and n have the same nonzero digits, irrespective of order. For example, a(6044005) = a(45604).
FORMULA
If n has digits n_1, n_2, ..., n_k and all digits n_i are even, then a(n) = (1/2)(n_1 + 1)(n_2 + 1)...(n_k + 1) - 1/2. Otherwise, a(n) = (1/2)(n_1 + 1)(n_2 + 1)...(n_k + 1) - 1. Equivalently, a(n) = ceiling((1/2)(n_1 + 1)(n_2 + 1)...(n_k + 1)) - 1 for all n.
a(n) = ceiling((1/2)*A089898(n)) - 1.
EXAMPLE
a(31) = 3 because there are three partitions of 31 into exactly two parts with no decimal carries: 30 + 1, 21 + 10, and 20 + 11.
a(100) = 0 because every partition of 100 into exactly two parts has at least one decimal carry.
MATHEMATICA
Ceiling[(1/2) Times @@ (IntegerDigits[n, 10] + 1)] - 1
CROSSREFS
Cf. A088512 (analogous sequence for base 2), A089898.
Sequence in context: A304706 A084054 A106747 * A083447 A252489 A357839
KEYWORD
nonn,base,easy
AUTHOR
Jason Zimba, Jul 02 2020
STATUS
approved