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%I #18 Jul 05 2020 15:21:14
%S 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,
%T 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,
%U 26,29,3,6,10,13,17,20,24,27,31,34,3,7,11,15,19,23
%N Number of partitions of n into exactly two parts with no decimal carries.
%C a(m) = a(n) if m and n have the same nonzero digits, irrespective of order. For example, a(6044005) = a(45604).
%F 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.
%F a(n) = ceiling((1/2)*A089898(n)) - 1.
%e 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.
%e a(100) = 0 because every partition of 100 into exactly two parts has at least one decimal carry.
%t Ceiling[(1/2) Times @@ (IntegerDigits[n, 10] + 1)] - 1
%Y Cf. A088512 (analogous sequence for base 2), A089898.
%K nonn,base,easy
%O 0,5
%A _Jason Zimba_, Jul 02 2020
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