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A182228 a(n) = 3*a(n-2) - a(n-1), a(0) = 0, a(1) = 1. 3
0, 1, -1, 4, -7, 19, -40, 97, -217, 508, -1159, 2683, -6160, 14209, -32689, 75316, -173383, 399331, -919480, 2117473, -4875913, 11228332, -25856071, 59541067, -137109280, 315732481, -727060321, 1674257764, -3855438727, 8878212019, -20444528200, 47079164257 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

This is A006130 with minus signs on every other term. - T. D. Noe, Apr 23 2012

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (-1,3).

FORMULA

a(n) = -A140167(n). G.f. x/(1+x-3*x^2). - R. J. Mathar, Apr 22 2013

G.f.: 1 - Q(0), where Q(k) = 1 + 3*x^2 - (k+2)*x + x*(k+1 - 3*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 06 2013

E.g.f.: (-1/sqrt(13))*(exp(-(1+sqrt(13))*x/2) - exp(-(1-sqrt(13))*x/2)). - G. C. Greubel, Aug 30 2015

MATHEMATICA

RecurrenceTable[{a[n]== - a[n-1] + 3*a[n-2], a[0]== 0, a[1]== 1}, a, {n, 0, 200}] (* G. C. Greubel, Aug 30 2015 *)

LinearRecurrence[{-1, 3}, {0, 1}, 40] (* Harvey P. Dale, Oct 23 2016 *)

PROG

(Python)

prpr = 0

prev = 1

for i in range(2, 55):

. current = prpr*3-prev

. print current,

. prpr = prev

. prev = current

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else (-1)*Self(n-1) + 3*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Aug 31 2015

CROSSREFS

Cf. A140167.

Sequence in context: A062306 A006130 A140167 * A182646 A190646 A220011

Adjacent sequences:  A182225 A182226 A182227 * A182229 A182230 A182231

KEYWORD

sign,easy

AUTHOR

Alex Ratushnyak, Apr 19 2012

STATUS

approved

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Last modified June 29 11:55 EDT 2017. Contains 288860 sequences.