Padovan sequence

In number theory, the Padovan sequence is the sequence of integers P(n) defined by the initial values: P ( 0 ) = P ( 1 ) = P ( 2 ) = 1 , {\displaystyle P(0)=P(1)=P(2)=1,} and the recurrence relation P ( n ) = P ( n − 2 ) + P ( n − 3 ) . {\displaystyle P(n)=P(n-2)+P(n-3).} The first few values of P(n) are 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, ... (sequence A000931 in the OEIS) The Padovan sequence is named after Richard Padovan who attributed its discovery to Dutch architect Hans van der Laan in his 1994 essay Dom. Hans van der Laan: Modern Primitive. The sequence was described by Ian Stewart in his Scientific American column Mathematical Recreations in June 1996. He also writes about it in one of his books, "Math Hysteria: Fun Games With Mathematics". The above definition is the one given by Ian Stewart and by MathWorld. Other sources may start the sequence at a different place, in which case some of the identities in this article must be adjusted with appropriate offsets.