SequencesSequencesMedium
Narayana's Cows
A 14th-century cattle puzzle hides a cousin of the Fibonacci sequence.
Worked demonstration
Narayana Pandita's cow problem gives a sequence where each term is the term before plus the term three places back: 1, 1, 1, 2, 3, 4, … What is the 10th term?
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Why it works
Each term is the previous term plus the term three places back: 1, 1, 1, 2, 3, 4, 6, 9, … — a third-order recurrence.
Background & Explore Further
Narayana Pandita's Ganita Kaumudi (1356) posed this; its ratio tends to the 'supergolden ratio'. Explore how Fibonacci's rabbits, Pingala's syllables and Narayana's cows all land on linear recurrences.