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A329227 Products of consecutive members of the Padovan sequence A000931. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Equal to A000931(n)*A000931(n+1).

LINKS

Table of n, a(n) for n=0..40.

FORMULA

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.

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.

Sequence in context: A307067 A060798 A134320 * A294430 A294429 A107383

Adjacent sequences:  A329224 A329225 A329226 * A329228 A329229 A329230

KEYWORD

nonn

AUTHOR

David Nacin, Nov 08 2019

STATUS

approved

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Last modified April 17 06:46 EDT 2021. Contains 343059 sequences. (Running on oeis4.)