A099035 a(n) = (n+1)*2^(n-1) - 1.

1, 5, 15, 39, 95, 223, 511, 1151, 2559, 5631, 12287, 26623, 57343, 122879, 262143, 557055, 1179647, 2490367, 5242879, 11010047, 23068671, 48234495, 100663295, 209715199, 436207615, 905969663, 1879048191, 3892314111, 8053063679

Offset: 1

Author

Ralf Stephan, Sep 28 2004

Keywords

• nonn
• easy

Comments

Row sums of triangle A135852. - Gary W. Adamson, Dec 01 2007

Binomial transform of [1, 4, 6, 8, 10, 12, 14, 16, ...]. Equals A128064 * A000225, (A000225 starting 1, 3, 7, 15, ...). - Gary W. Adamson, Dec 28 2007

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Crossrefs

First differences of A066524.

Cf. A135852, A128064, A000225.

Programs

Magma

[(n+1)*2^(n-1) -1: n in [1..30]]; // G. C. Greubel, Dec 31 2017

Mathematica

Table[(n + 1)*2^(n - 1) - 1, {n,1,30}] (* G. C. Greubel, Dec 31 2017 *)
LinearRecurrence[{5,-8,4},{1,5,15},30] (* Harvey P. Dale, Dec 28 2022 *)

PARI

a(n)=(n+1)*2^(n-1)-1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = A057711(n+1) - 1 = A058966(n+3)/2 = (A087323(n)-1)/2 = (A074494(n+1)-2)/3 = (A003261(n+1)-3)/4 = A036289(n+1)/4 - 1, n>0.

a(n) = A131056(n+1) - 2. - Juri-Stepan Gerasimov, Oct 02 2011

From Colin Barker, Mar 23 2012: (Start)

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3).

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

E.g.f.: ((2*x+1)*exp(2*x) - 2*exp(x) + 1)/2. - G. C. Greubel, Dec 31 2017