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A077859 Expansion of (1-x)^(-1)/(1-2*x+2*x^2-x^3). 6
1, 3, 5, 6, 6, 6, 7, 9, 11, 12, 12, 12, 13, 15, 17, 18, 18, 18, 19, 21, 23, 24, 24, 24, 25, 27, 29, 30, 30, 30, 31, 33, 35, 36, 36, 36, 37, 39, 41, 42, 42, 42, 43, 45, 47, 48, 48, 48, 49, 51, 53, 54, 54, 54, 55, 57, 59, 60, 60, 60, 61, 63, 65, 66, 66, 66, 67, 69, 71, 72, 72, 72, 73, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A021823. Second partial sums of A010892. - Paul Barry, Jun 06 2003

Row sums of A144083 [Gary W. Adamson, Sep 10 2008]

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (3,-4,3,-1).

FORMULA

G.f.: 1/((1-x)^2*(1-x+x^2)).

a(n) = sum{k=0..n, (k+1)*2sin(pi(n-k)/3+pi/3)/sqrt(3). - Paul Barry, May 18 2004

a(n) = sum{k=0..n, binomial(n-2k, n-k-1)}; - Paul Barry, Jan 15 2005

a(n) = n+2+(-1+n-3*floor(n/3))*(-1)^floor(n/3). - Tani Akinari, Jun 27 2013

a(n) = n + 1 + a(n-1) - a(n-2), with a(-1) = a(-2) = 0. - Richard R. Forberg, Jul 11 2013

a(n) = +3*a(n-1) -4*a(n-2) +3*a(n-3) -1*a(n-4). [Joerg Arndt, Jul 12 2013]

a(n) = sum{k=0..n, (-1)^k*(n+1-k)*b(k)}, where b(n)=A049347(n). - Mircea Merca, Feb 04 2014

MAPLE

A010892 := proc(n) op(1+(n mod 6), [1, 1, 0, -1, -1, 0]) ; end proc:

A077859 := proc(n) n+2+A010892(n+4) ; end proc:

seq(A077859(n), n=0..50) ; # R. J. Mathar, Mar 22 2011

MATHEMATICA

s=0; w1=0; w2=0; lst={w1, w2}; Do[s+=n-w1; AppendTo[lst, s]; w1=w2; w2=s, {n, 0, 2*5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 26 2008 *)

CoefficientList[Series[(1 - x)^(-1)/(1 - 2 x + 2 x^2 - x^3), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 04 2014 *)

PROG

(PARI) Vec(1/(1-x)/(1-2*x+2*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012

(MAGMA) I:=[1, 3, 5, 6]; [n le 4 select I[n] else 3*Self(n-1)-4*Self(n-2)+3*Self(n-3)-Self(n-4): n in [1..100]]

CROSSREFS

Cf. A010892, A021823, A144083.

Sequence in context: A224831 A281591 A267884 * A123572 A244953 A076819

Adjacent sequences:  A077856 A077857 A077858 * A077860 A077861 A077862

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)