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

0,1

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).

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)

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 *)

Prog

(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

Crossrefs

Cf. A053016.

Sequence in context: A078785 A308875 A323059 * A146528 A345016 A216051

Adjacent sequences: A136251 A136252 A136253 * A136255 A136256 A136257

Keyword

nonn,easy

Author

Rolf Pleisch, Mar 17 2008

Status

approved