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A009759 Expansion of (3-21*x+4*x^2)/((x-1)*(x^2-6*x+1)). 1
-3, 0, 17, 116, 693, 4056, 23657, 137900, 803757, 4684656, 27304193, 159140516, 927538917, 5406093000, 31509019097, 183648021596, 1070379110493, 6238626641376, 36361380737777, 211929657785300, 1235216565974037 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Numbers n such that 2*n^2 + 14*n + 25 is the square of an integer. - James R. Buddenhagen, Jul 19 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

FORMULA

a(n) = A001652(n)-3.

a(n) = ( (1+sqrt(2))^(2*n+1) + (1-sqrt(2))^(2*n+1) - 14 )/4.

a(n) - a(n-1) = A001541(n), n>0. - R. J. Mathar, Apr 23 2009

MATHEMATICA

CoefficientList[Series[(3-21x+4x^2)/((x-1)(x^2-6x+1)), {x, 0, 30}], x] (* or *) LinearRecurrence[{7, -7, 1}, {-3, 0, 17}, 30] (* Harvey P. Dale, Dec 12 2016 *)

PROG

(PARI) x='x+O('x^30); Vec((3-21*x+4*x^2)/((x-1)*(x^2-6*x+1))) \\ G. C. Greubel, Feb 12 2018

(MAGMA) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((3-21*x+4*x^2)/((x-1)*(x^2-6*x+1)))) // G. C. Greubel, Feb 12 2018

CROSSREFS

Cf. A001652.

Sequence in context: A036968 A226158 A024040 * A127187 A057398 A013579

Adjacent sequences:  A009756 A009757 A009758 * A009760 A009761 A009762

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nick Baxter (nick(AT)visigenic.com)

EXTENSIONS

G.f. and Binet formula corrected by R. J. Mathar, Aug 24 2016

STATUS

approved

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Last modified February 15 16:25 EST 2019. Contains 320136 sequences. (Running on oeis4.)