A335979 Number of partitions of n into exactly two parts with no decimal carries.

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).

Links

Table of n, a(n) for n=0..75.

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

Adjacent sequences: A335976 A335977 A335978 * A335980 A335981 A335982

Keyword

nonn,base,easy

Author

Jason Zimba, Jul 02 2020

Status

approved