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Palindromic partitioning of the natural number

A

is called, when

A

is written as the sum of natural the terms

A = a_1 + a_2 + \ ldots + a_ {n-1} + a_n

(

n \geq 1

), in which

a_1 = a_n , a_2 = a_ {n-1}

and in general,

a_i = a_ {n + 1 - i}

with

1 \leq i \leq n

. For example,

16 = 16

16 = 2 + 12 + 2

and

16 = 7 + 1 + 1 + 7

are palindromic partitions of the number

16

. Find the number of all palindromic partitions of the number

2006

Problem Statement