A126284 a(n) = 5*2^n - 4*n - 5.

1, 7, 23, 59, 135, 291, 607, 1243, 2519, 5075, 10191, 20427, 40903, 81859, 163775, 327611, 655287, 1310643, 2621359, 5242795, 10485671, 20971427, 41942943, 83885979, 167772055, 335544211, 671088527, 1342177163, 2684354439

Offset: 1

Author

Gary W. Adamson, Dec 24 2006

Keywords

• nonn
• easy

Comments

Row sums of A125233.

A triangle with left and right borders being the odd numbers 1,3,5,7,... will give the same partial sums for the sum of its rows. - J. M. Bergot, Sep 29 2012

The triangle in the above comment is constructed the same way as Pascal's triangle, i.e., C(n, k) = C(n-1, k) + C(n-1, k-1). - Michael B. Porter, Oct 03 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A000384, A125233, A126277.

Programs

GAP

List([1..30],n->5*2^n-4*n-5); # Muniru A Asiru, Oct 24 2018

Magma

[5*2^n - 4*n - 5: n in [1..30]]; // G. C. Greubel, Oct 23 2018

Maple

A126284:=n->5*2^n-4*n-5; seq(A126284(n), n=1..50); # Wesley Ivan Hurt, Mar 27 2014

Mathematica

CoefficientList[Series[(1 + 3 x)/(1 - 4 x + 5 x^2 - 2 x^3), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 28 2014 *)

PARI

a(n)=5<Charles R Greathouse IV, Oct 03 2012

Formula

a(1) = 1; a(2) = 7; a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3), n > 2.

The 6th diagonal from the right of A126277.

G.f.: x*(1+3*x)/(1-4*x+5*x^2-2*x^3). - Colin Barker, Feb 12 2012

E.g.f.: 5*exp(2*x) - (5+4*x)*exp(x). - G. C. Greubel, Oct 23 2018

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Oct 18 2008

New definition from R. J. Mathar, Sep 29 2012