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A329227 Products of consecutive terms of the Padovan sequence A000931. 3

%I #16 Jul 05 2021 16:46:12

%S 0,0,0,0,0,1,1,2,4,6,12,20,35,63,108,192,336,588,1036,1813,3185,5590,

%T 9804,17214,30200,53000,93015,163215,286440,502656,882096,1547992,

%U 2716504,4767161,8365777,14680890,25763220,45211238,79340228,139232412,244335771

%N Products of consecutive terms of the Padovan sequence A000931.

%H Harvey P. Dale, <a href="/A329227/b329227.txt">Table of n, a(n) for n = 0..1000</a>

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

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

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

%F G.f.: x^5 / ((1 - 2*x + x^2 - x^3)*(1 + x - x^3)) (conjectured). - _Colin Barker_, Nov 08 2019

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

%t Times@@@Partition[LinearRecurrence[{0,1,1},{1,0,0},50],2,1] (* _Harvey P. Dale_, Jul 05 2021 *)

%o (Python)

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

%o a = lambda x:p(x)*p(x+1)

%Y Cf. A000931, A133037.

%K nonn

%O 0,8

%A _David Nacin_, Nov 08 2019

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)