

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
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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(n1)  6*a(n2) + 4*a(n3)  a(n4). (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



