A136254 Generator for the finite sequence A053016.

4, 6, 8, 12, 20, 34, 56, 88, 132, 190, 264, 356, 468, 602, 760, 944, 1156, 1398, 1672, 1980, 2324, 2706, 3128, 3592, 4100, 4654, 5256, 5908, 6612, 7370, 8184, 9056, 9988, 10982, 12040, 13164, 14356

Offset: 0

Author

Rolf Pleisch, Mar 17 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A053016.

Programs

Mathematica

CoefficientList[Series[(8*x^2 - 10*x + 4)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1), {x, 0, 50}], x] (* G. C. Greubel, Feb 23 2017 *)
LinearRecurrence[{4,-6,4,-1},{4,6,8,12},40] (* Harvey P. Dale, Jul 23 2018 *)

PARI

x='x+O('x^50); Vec((8*x^2 - 10*x + 4)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1)) \\ G. C. Greubel, Feb 23 2017

Formula

a(n) = n^3/3 - n^2 + 8n/3 + 4.

G.f.: (8*x^2 - 10*x + 4)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1). - Alexander R. Povolotsky, Mar 31 2008

From G. C. Greubel, Feb 23 2017: (Start)

E.g.f.: (1/3)*(12 + 6*x + x^3)*exp(x).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)