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A052938 Expansion of ( 1+2*x-2*x^2 ) / ( (1+x)*(x-1)^2 ). 11
1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 20, 19, 21, 20, 22, 21, 23, 22, 24, 23, 25, 24, 26, 25, 27, 26, 28, 27, 29, 28, 30, 29, 31, 30, 32, 31, 33, 32, 34, 33, 35, 34, 36, 35, 37, 36, 38, 37, 39 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A035106(n+3) - A035106(n+2). - Reinhard Zumkeller, Oct 06 2015

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 929

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

FORMULA

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

Recurrence: {a(0)=1, a(2)=2, a(1)=3, a(n)+a(n+1)-n-4 =0}

a(n) = (3/4)*(-1)^(1-n) + (1/2)*n + 7/4.

A112034(n) = 3*2^a(n); a(n) = A109613(n+2) - A084964(n). - Reinhard Zumkeller, Aug 27 2005

a(n) = A060762(n+1) - 1. - Filip Zaludek, Nov 19 2016

MAPLE

spec := [S, {S=Prod(Union(Sequence(Z), Z, Z), Sequence(Prod(Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);

PROG

(PARI) a(n)=([0, 1, 0; 0, 0, 1; -1, 1, 1]^n*[1; 3; 2])[1, 1] \\ Charles R Greathouse IV, Sep 02 2015

(Haskell)

a052938 n = a052938_list !! n

a052938_list = 1 : 3 : 2 : zipWith (-) [5..] a052938_list

-- Reinhard Zumkeller, Oct 06 2015

CROSSREFS

Cf. A028242 (same sequence with 1,0,2 prefix).

Cf. A035106.

Sequence in context: A134559 A007456 A119707 * A140114 A243852 A025532

Adjacent sequences:  A052935 A052936 A052937 * A052939 A052940 A052941

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

More terms from James A. Sellers, Jun 06 2000

STATUS

approved

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Last modified December 14 21:25 EST 2017. Contains 296020 sequences.