A142964 a(n) = 6*2^n - 2*n - 5.

1, 5, 15, 37, 83, 177, 367, 749, 1515, 3049, 6119, 12261, 24547, 49121, 98271, 196573, 393179, 786393, 1572823, 3145685, 6291411, 12582865, 25165775, 50331597, 100663243, 201326537, 402653127, 805306309, 1610612675, 3221225409, 6442450879, 12884901821

Offset

0,2

Comments

Previous name was: One half of second column (m=1) of triangle A142963.

Essentially a duplicate of A050488. - Johannes W. Meijer, Feb 20 2009

References

Eric Billault, Walter Damin, Robert Ferréol, Rodolphe Garin, MPSI Classes Prépas - Khôlles de Maths, Exercices corrigés, Ellipses, 2012, exercice 2.22 (1) pp 26, 43-44.

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(n) = A142693(n+2,1)/2.

From Johannes W. Meijer, Feb 20 2009: (Start)

a(n) = 4a(n-1) - 5a(n-2) + 2a(n-3) for n > 2 with a(0) = 1, a(1) = 5, a(2) = 15.

G.f.: (1+z)/((1-z)^2*(1-2*z)). (End)

a(n) = Sum_{i=0..n} Sum_{j=0..n} 2^min(i,j) (Billault et al) (compare with A339771 that has max instead of min). - Bernard Schott, Dec 16 2020

a(n) = 2*A066524(n+1) - A339771(n). - Kevin Ryde, Dec 17 2020

E.g.f.: 6*exp(2*x) - exp(x)*(5 + 2*x). - Stefano Spezia, Dec 17 2020

Example

a(3) = 6*2^3 - 2*3 - 5 = 37.

Maple

seq(6*2^n-2*n-5, n=0..40); # Bernard Schott, Dec 16 2020

Prog

(PARI) Vec((1+z)/((1-z)^2*(1-2*z)) + O(z^50)) \\ Michel Marcus, Jun 18 2017

Crossrefs

Cf. A142965 (m=2 column/4).

Equals A050488(n+1).

Equals A156920(n+1,1).

Equals A156919(n+1,1)/2^n.

Cf. A156925, A339771.

Partial sums of A033484.

Sequence in context: A213487 A005491 A348780 * A050488 A188282 A014316

Adjacent sequences: A142961 A142962 A142963 * A142965 A142966 A142967

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 15 2008

Extensions

New name using a formula of Bernard Schott by Peter Luschny, Dec 17 2020

Status

approved