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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)