A291289 The Padovan sequence A000931 doubled.

2, 0, 0, 2, 0, 2, 2, 2, 4, 4, 6, 8, 10, 14, 18, 24, 32, 42, 56, 74, 98, 130, 172, 228, 302, 400, 530, 702, 930, 1232, 1632, 2162, 2864, 3794, 5026, 6658, 8820, 11684, 15478, 20504, 27162, 35982, 47666, 63144, 83648, 110810, 146792, 194458, 257602, 341250

Offset

0,1

Comments

Like A000931, this sequence has the property that the largest of any four consecutive terms equals the sum of the two smallest.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..8192

David Nacin, Van der Laan Sequences and a Conjecture on Padovan Numbers, J. Int. Seq., Vol. 26 (2023), Article 23.1.2.

Index entries for linear recurrences with constant coefficients, signature (0,1,1).

Formula

G.f.: 2*(1-x^2)/(1-x^2-x^3).

Mathematica

CoefficientList[Series[2*(1 - x^2)/(1 - x^2 - x^3), {x, 0, 49}], x] (* Michael De Vlieger, Mar 21 2023 *)

Crossrefs

Cf. A000931.

Sequence in context: A289323 A086937 A213024 * A095759 A260309 A046113

Adjacent sequences: A291286 A291287 A291288 * A291290 A291291 A291292

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 29 2017

Status

approved