A336430 Number of partitions of n into two positive integer parts that have the same number of decimal digits.

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30

Offset

1,4

Links

Table of n, a(n) for n=1..79.

Formula

a(n) = Sum_{k=1..floor(n/2)} [floor(log_10(k)) = floor(log_10(n-k))], where [ ] is the Iverson bracket.

Example

a(11) = 4; There are 5 partitions of 11 into two parts, (10,1), (9,2), (8,3), (7,4) and (6,5). Only 4 of these partitions have the same number of decimal digits, so a(11) = 4.

Mathematica

Table[Sum[KroneckerDelta[Floor[Log10[i]], Floor[Log10[n - i]]], {i, Floor[n/2]}], {n, 100}]

Crossrefs

Cf. A055642.

Sequence in context: A219773 A187446 A240020 * A395818 A368086 A167232

Adjacent sequences: A336427 A336428 A336429 * A336431 A336432 A336433

Keyword

nonn,base,easy

Author

Wesley Ivan Hurt, Dec 21 2020

Status

approved