This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335979 #18 Jul 05 2020 15:21:14 %S A335979 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 A335979 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 A335979 26,29,3,6,10,13,17,20,24,27,31,34,3,7,11,15,19,23 %N A335979 Number of partitions of n into exactly two parts with no decimal carries. %C A335979 a(m) = a(n) if m and n have the same nonzero digits, irrespective of order. For example, a(6044005) = a(45604). %F A335979 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 A335979 a(n) = ceiling((1/2)*A089898(n)) - 1. %e A335979 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 A335979 a(100) = 0 because every partition of 100 into exactly two parts has at least one decimal carry. %t A335979 Ceiling[(1/2) Times @@ (IntegerDigits[n, 10] + 1)] - 1 %Y A335979 Cf. A088512 (analogous sequence for base 2), A089898. %K A335979 nonn,base,easy %O A335979 0,5 %A A335979 _Jason Zimba_, Jul 02 2020