A329178 Sum of the products of pairs of Padovan numbers which are two apart, starting from A000931(5).

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

Links

Table of n, a(n) for n=0..35.

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

Cf. A000931, A133037, A329227.

Sequence in context: A092602 A134127 A239519 * A298348 A303005 A320790

Adjacent sequences: A329175 A329176 A329177 * A329179 A329180 A329181

Keyword

nonn

Author

David Nacin, Nov 08 2019

Status

approved