A173855 a(n) = A173039(n+4) - A173039(n+1).

8, 4, 24, 40, 12, 56, 72, 20, 88, 104, 28, 120, 136, 36, 152, 168, 44, 184, 200, 52, 216, 232, 60, 248, 264, 68, 280, 296, 76, 312, 328, 84, 344, 360, 92, 376, 392, 100, 408, 424, 108, 440, 456, 116, 472, 488, 124, 504, 520, 132, 536, 552, 140, 568, 584, 148

Offset: 1

Author

Paul Curtz, Nov 26 2010

Keywords

• nonn
• easy

Comments

From Balmer odd terms. Note that ( (a(n+1)=8,) - (Balmer A061037 odd numbers = A173039(n+4) = 5, ) = 3, 1, 3, -5, -3, -21, ... = -A173039.

Examples

			a(1) = 5 - (-3) = 8, a(2) = 3 - (-1) = 4, a(3) = 21 - (-3) = 24.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A017113, A173039, A173773.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(4*x*(x+1)*(2*x^4-x^3+7*x^2-x+2)/((x-1)^2*(x^2+x+1)^2))); // G. C. Greubel, Sep 20 2018

Maple

a:= LREtools[REtoproc](f(n) = 2*f(n-3)-f(n-6), f(n), zip((s,t)->f(s)=t, [$1..6],[8,4,24,40,12,56]),remember):
seq(a(n), n=1..100); # Robert Israel, Oct 15 2014

Mathematica

Rest[CoefficientList[Series[4*x*(x+1)*(2*x^4-x^3+7*x^2-x+2)/((x-1)^2*(x^2 +x+1)^2), {x, 0, 50}], x]] (* G. C. Greubel, Sep 20 2018 *)

PARI

Vec(4*x*(x+1)*(2*x^4-x^3+7*x^2-x+2)/((x-1)^2*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Oct 15 2014

Formula

a(n) = 4*A173773(n).

a(n) = 2*a(n-3) - a(n-6). - Colin Barker, Oct 15 2014

G.f.: 4*x*(x+1)*(2*x^4 - x^3 + 7*x^2 - x + 2) / ((x-1)^2*(x^2 + x + 1)^2). - Colin Barker, Oct 15 2014

Extensions

More terms from Colin Barker, Oct 15 2014