

A336430


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


0



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
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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(nk))], 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 * A167232 A319468 A137791
Adjacent sequences: A336427 A336428 A336429 * A336431 A336432 A336433


KEYWORD

nonn,base,easy


AUTHOR

Wesley Ivan Hurt, Dec 21 2020


STATUS

approved



