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

Author

N. J. A. Sloane, Aug 29 2017

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000931.

Programs

Mathematica

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

Formula

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