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URL: https://oeis.org/A329178

⇱ A329178 - OEIS

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A329178
Sum of the products of pairs of Padovan numbers which are two apart, starting from A000931(5).
0
1, 3, 5, 11, 19, 34, 62, 107, 191, 335, 587, 1035, 1812, 3184, 5589, 9803, 17213, 30199, 52999, 93014, 163214, 286439, 502655, 882095, 1547991, 2716503, 4767160, 8365776, 14680889, 25763219, 45211237, 79340227, 139232411, 244335770, 428779502, 752455475
OFFSET
0,2
FORMULA
a(n) = Sum_{i=5..n+5} A000931(i)*A000931(i+2).
a(n) = A329227(n+7) - 1.
Conjectures from Colin Barker, Nov 09 2019: (Start)
G.f.: (1 + x - x^2 + x^3 - x^4) / ((1 - x)*(1 - 2*x + x^2 - x^3)*(1 + x - x^3)).
a(n) = 2*a(n-1) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + a(n-7) for n>6.
(End)
EXAMPLE
For n=3, a(3) = 1*1 + 1*2 + 1*2 + 2*3 = 11.
PROG
(Python)
p = lambda x:[1, 1, 1][x] if x<3 else p(x-2)+p(x-3)
a = lambda x:sum(p(i)*p(i+2) for i in range(x+1))
CROSSREFS
KEYWORD
nonn
AUTHOR
David Nacin, Nov 08 2019
STATUS
approved