The Padovan sequence is the sequence of integers P(n) defined by the initial values
and the recurrence relation
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 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.
Read more about Padovan Sequence: Recurrence Relations, Extension To Negative Parameters, Sums of Terms, Other Identities, Binet-like Formula, Combinatorial Interpretations, Generating Function, Generalizations, Padovan Prime, Padovan L-system, Padovan Cuboid Spiral
Famous quotes containing the word sequence:
“We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.”
—E.M. (Edward Morgan)