The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A033505 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A033505

Expansion of 1/(1 - 3*x - x^2 + x^3).
(history; published version)

#35 by N. J. A. Sloane at Fri Dec 27 03:24:13 EST 2019

STATUS

editing

approved

#34 by N. J. A. Sloane at Fri Dec 27 03:24:10 EST 2019

LINKS

N. J. A. Sloane <a href="/A030186/a030186.txt">Notes on A030186 and A033505</a>

STATUS

approved

editing

#33 by Andrew Howroyd at Tue Oct 15 12:24:38 EDT 2019

STATUS

reviewed

approved

#32 by Michel Marcus at Mon Oct 14 12:27:42 EDT 2019

STATUS

proposed

reviewed

#31 by G. C. Greubel at Mon Oct 14 12:06:14 EDT 2019

STATUS

editing

proposed

#30 by G. C. Greubel at Mon Oct 14 12:06:04 EDT 2019

MAPLE

seq(coeff(series(1/(1-3*x-x^2+x^3), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 14 2019

MATHEMATICA

CoefficientList[Series[1/(1 - 3 x 3x- x^2 + x^3), {x, 0, 3330}], x] (* or *) LinearRecurrence[{3, 1, -1}, {1, 3, 10}, 30] (* Vincenzo Librandi, Aug 17 2018 *)

PROG

(PARI) my(x='x+O('x^30)); Vec(1/(1-3*x-x^2+x^3)) \\ G. C. Greubel, Oct 14 2019

(Sage)

def A033505_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P(1/(1-3*x-x^2+x^3)).list()

A033505_list(30) # G. C. Greubel, Oct 14 2019

(GAP) a:=[1, 3, 10];; for n in [4..30] do a[n]:=3*a[n-1]+a[n-2]-a[n-3]; od; a; # G. C. Greubel, Oct 14 2019

STATUS

approved

editing

#29 by Joerg Arndt at Tue Aug 21 05:56:31 EDT 2018

STATUS

reviewed

approved

#28 by Michel Marcus at Tue Aug 21 05:33:24 EDT 2018

STATUS

proposed

reviewed

#27 by Vincenzo Librandi at Fri Aug 17 02:02:56 EDT 2018

STATUS

editing

proposed

#26 by Vincenzo Librandi at Fri Aug 17 02:02:16 EDT 2018

DATA

1, 3, 10, 32, 103, 331, 1064, 3420, 10993, 35335, 113578, 365076, 1173471, 3771911, 12124128, 38970824, 125264689, 402640763, 1294216154, 4160024536, 13371648999, 42980755379, 138153890600, 444070778180, 1427385469761, 4588073296863, 14747534582170

LINKS

Vincenzo Librandi, <a href="/A033505/b033505.txt">Table of n, a(n) for n = 0..1000</a>

MATHEMATICA

CoefficientList[Series[1/(1 - 3 x - x^2 + x^3), {x, 0, 33}], x] (* or *) LinearRecurrence[{3, 1, -1}, {1, 3, 10}, 30] (* Vincenzo Librandi, Aug 17 2018 *)

PROG

(MAGMA) I:=[1, 3, 10]; [n le 3 select I[n] else 3*Self(n-1)+Self(n-2)-Self(n-3): n in [1..30]]; // Vincenzo Librandi, Aug 17 2018

STATUS

proposed

editing