A238290 a(n+1) = a(n) + 6 + 2*(n - 2*floor(n/2)) for n > 0, a(0) = 0.

0, 8, 14, 22, 28, 36, 42, 50, 56, 64, 70, 78, 84, 92, 98, 106, 112, 120, 126, 134, 140, 148, 154, 162, 168, 176, 182, 190, 196, 204, 210, 218, 224, 232, 238, 246, 252, 260, 266, 274, 280, 288, 294, 302, 308, 316, 322, 330, 336, 344, 350, 358, 364, 372, 378

Offset: 0

Author

Jose Eduardo Blazek, Feb 22 2014

Keywords

• nonn
• easy

Examples

			G.f.: 8*x + 14*x^2 + 22*x^3 + 28*x^4 + 36*x^5 + 42*x^6 + 50*x^7 + 56*x^8 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Crossrefs

Cf. A047345.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(2*x*(4+3*x)/((1-x)*(1-x^2)))); // G. C. Greubel, Aug 07 2018

Mathematica

CoefficientList[Series[2 x (4 + 3 x)/((1 - x) (1 - x^2)), {x, 0, 80}], x] (* Vincenzo Librandi, Feb 26 2014 *)
Table[(14 n - (-1)^n + 1)/2, {n, 0, 60}] (* Bruno Berselli, Feb 26 2014 *)

PARI

x='x+O('x^50); concat([0], Vec(2*x*(4+3*x)/((1-x)*(1-x^2)))) \\ G. C. Greubel, Aug 07 2018

Formula

a(n) = floor((2*n+1)/4) + 2*floor((2*n+1)/2) + 3*floor(3*(2*n+1)/4).

a(n) = 8*floor((n+1)/2) + 6*floor(n/2).

G.f.: 2 * x * (4 + 3*x) / ((1 - x) * (1 - x^2)). - Michael Somos, Feb 24 2014

a(n) = 2*A047345(n+1) = (14*n - (-1)^n + 1)/2. - Bruno Berselli, Feb 26 2014

E.g.f.: 7*exp(x)*x + sinh(x). - Stefano Spezia, May 15 2021