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

0,8

Links

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

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

Example

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

Mathematica

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

Prog

(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)

Crossrefs

Cf. A000931, A133037.

Sequence in context: A060798 A134320 A353561 * A294430 A294429 A107383

Adjacent sequences: A329224 A329225 A329226 * A329228 A329229 A329230

Keyword

nonn

Author

David Nacin, Nov 08 2019

Status

approved