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Let us see the horizontal sum of numbers in each row.

Horizontal sum = 1

Horizontal sum = 1 + 1 = 2

Horizontal sum = 1 + 2 + 1 = 4

Horizontal sum = 1 + 3 + 3 + 1 = 8

Horizontal sum = 1 + 4 + 6 + 4 + 1 = 16

Horizontal sum = 1 + 5 + 10 + 10 + 5 + 1 = 32

Look at the sum obtained:
1, 2, 4, 8, 16, 32, ... which are the power of 2, because each next row sum is twice the sum of
previous row.
Conclusion: Sum of numbers of nth row = 2 × 2 × 2 × 2 × ... n times.
The conclusion is a conjecture.

A Pinch of History

Indian Connection to Pascal Triangle: The first records relating to Pascal’s Triangle come from India.
Pingala was a famous mathematician from India around 200 BCE (Crystal Clear Mathematics). He wrote
a book called Chhandashastra where he connected mathematics to Sanskrit poetry (Shah). As he worked
with the relationship between meters and syllables, he found an algorithm for combinatorics. Pingala’s
work was expanded on for years afterwards. There are disputes about whether his work directly led to
a version of Pascal’s Triangle, but a mathematician named Halayudha from the 10th century CE claims
that Pingala’s last sutra explains the construction of such a triangle. Halayudha is the one to give detailed
instructions about what they call Meru-Prastara or the Staircase of Mount Meru.

Prakrit Pingala Prastara, Raghunath Temple, Jammu

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