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A136254 Generator for the finite sequence A053016. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A216051 A176777

Adjacent sequences:  A136251 A136252 A136253 * A136255 A136256 A136257

KEYWORD

nonn

AUTHOR

Rolf Pleisch, Mar 17 2008

STATUS

approved

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Last modified December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)