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

1,2

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).

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

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 *)

Prog

(PARI) a(n)=5<<n-4*n-5 \\ Charles R Greathouse IV, Oct 03 2012
(Magma) [5*2^n - 4*n - 5: n in [1..30]]; // G. C. Greubel, Oct 23 2018
(GAP) List([1..30], n->5*2^n-4*n-5); # Muniru A Asiru, Oct 24 2018

Crossrefs

Cf. A000384, A125233, A126277.

Sequence in context: A213770 A235683 A037165 * A140096 A096345 A211644

Adjacent sequences: A126281 A126282 A126283 * A126285 A126286 A126287

Keyword

nonn,easy

Author

Gary W. Adamson, Dec 24 2006

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Oct 18 2008

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

Status

approved