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A329227
Products of consecutive terms of the Padovan sequence A000931.
3
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
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
Sequence in context: A060798 A134320 A353561 * A294430 A294429 A107383
KEYWORD
nonn
AUTHOR
David Nacin, Nov 08 2019
STATUS
approved