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A011377 Expansion of 1/((1-x)*(1-2*x)*(1-x^2)). 12
1, 3, 8, 18, 39, 81, 166, 336, 677, 1359, 2724, 5454, 10915, 21837, 43682, 87372, 174753, 349515, 699040, 1398090, 2796191, 5592393, 11184798, 22369608, 44739229, 89478471, 178956956, 357913926 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

FORMULA

From Paul Barry, Jul 29 2004: (Start)

a(n) = Sum_{k=0..(n+2)} floor((n-k+2)/2) * 2^k ) =

a(n) = Sum_{k=0..(n+2)} floor(k/2) * 2^(n-k+2) ). (End)

a(n) = Sum_{k=0..floor((n+2)/2)} binomial(n-k+2, k+2)*2^k ). - Paul Barry, Oct 25 2004

a(n) = floor((2^(n+4)-3*n-6)/6). - David W. Wilson, Feb 26 2006

a(n) = (2^(n+5) - 6*n - 21 + (-1)^n)/12 - Hieronymus Fischer, Dec 02 2006

Row sums of triangle A135086. - Gary W. Adamson, Nov 18 2007

a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +2*a(n-4). - Paul Curtz, Jul 29 2008

G.f.: Q(0)/(3*x*(1-x)^2), where Q(k)= 1 - 1/(4^k - 2*x*16^k/(2*x*4^k - 1/(1 + 1/(2*4^k - 8*x*16^k/(4*x*4^k + 1/Q(k+1)))))); (continued fraction). - Sergei N. Gladkovskii, May 21 2013

MATHEMATICA

Join[{a=1, b=3}, Table[c=1*b+2*a+n; a=b; b=c, {n, 3, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 29 2011 *)

CoefficientList[Series[1/((1-x)(1-2x)(1-x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, -1, -3, 2}, {1, 3, 8, 18}, 30] (* Harvey P. Dale, Apr 17 2017 *)

PROG

(MAGMA) [Floor((2^(n+4)-3*n-6)/6): n in [0..40]]; // Vincenzo Librandi, Aug 14 2011

(PARI) x='x+O('x^50); Vec(1/((1-x)*(1-2*x)*(1-x^2))) \\ G. C. Greubel, Sep 26 2017

CROSSREFS

Partial sums of A000975.

Second partial sums of A001045.

Cf. A135086.

Sequence in context: A117713 A128552 A238361 * A178420 A036385 A196534

Adjacent sequences:  A011374 A011375 A011376 * A011378 A011379 A011380

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 17 16:53 EST 2019. Contains 319235 sequences. (Running on oeis4.)