A329227 Products of consecutive terms of the Padovan sequence A000931.

0, 0, 0, 0, 0, 1, 1, 2, 4, 6, 12, 20, 35, 63, 108, 192, 336, 588, 1036, 1813, 3185, 5590, 9804, 17214, 30200, 53000, 93015, 163215, 286440, 502656, 882096, 1547992, 2716504, 4767161, 8365777, 14680890, 25763220, 45211238, 79340228, 139232412, 244335771

Offset: 0

Author

David Nacin, Nov 08 2019

Keywords

• nonn

Examples

			For n=5, a(5) = A000931(5)*A000931(6) = 1*1.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000931, A133037.

Programs

Mathematica

Times@@@Partition[LinearRecurrence[{0,1,1},{1,0,0},50],2,1] (* Harvey P. Dale, Jul 05 2021 *)

Python

p = lambda x:[1,0,0][x] if x<3 else p(x-2)+p(x-3)
a = lambda x:p(x)*p(x+1)

Formula

a(n) = A000931(n)*A000931(n+1).

a(n+2) = Sum_{i=0..n} A000931(i)*A000931(i+2).

a(n) - a(n-2) - a(n-3) - a(n-4) = A133037(n-2) + A133037(n-3) for n>3.

G.f.: x^5 / ((1 - 2*x + x^2 - x^3)*(1 + x - x^3)) (conjectured). - Colin Barker, Nov 08 2019