$51 = 3 \times 17$
$51$ is the sixth Motzkin Number. A Motzkin number is the number of different ways of drawing non-intersecting chords on a circle between n points on the circle's circumference. Here I will unashamedly copy the illustration from Wikipedia which shows that when $n = 4$ the Motzkin number is $9$ i.e. there are $9$ different ways to draw lines connecting $4$ points, not necessarily all of the four points, on the circumference of a circle without the lines intersecting.
1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019, 142547559
Like the Fibonacci sequence, this sequence has a relationship that links the next number in the sequence to the previous two numbers. This relation is
$M_{n+1}=\frac{2n+3}{n+3}M_n+\frac{3n}{n+3}M_{n-1}$.
Thus
$M_6 = \frac{2.5+3}{5+3}M_5+\frac{3.5}{5+3}M_4$
knowing that $M_5 = 21$ and $M_4 = 9$ from the list above we get
$M_6 = \frac{13}{8}.21+\frac{15}{8}.9$
$M_6 = \frac {1} {8} (13. 21 + 15 . 9)$
$M_6 = \frac {1} {8} (273 + 135)$
$M_6 = \frac {1} {8} . 408$
Thus
$M_6 = 51$
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