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A098601 Expansion of (1+2x)/((1+x)(1-x^2-x^3)). 2
1, 1, 0, 3, 0, 4, 2, 5, 5, 8, 9, 14, 16, 24, 29, 41, 52, 71, 92, 124, 162, 217, 285, 380, 501, 666, 880, 1168, 1545, 2049, 2712, 3595, 4760, 6308, 8354, 11069, 14661, 19424, 25729, 34086, 45152, 59816, 79237, 104969, 139052, 184207, 244020, 323260 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Diagonal sums of A098599.

The signed sequence 1,-1,0,-3,0,-4,... gives the diagonal sums of A100218. - Paul Barry, Nov 09 2004

LINKS

Table of n, a(n) for n=0..47.

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

FORMULA

G.f.: x/((1+x)(1-x^2-x^3))+1/(1-x^2-x^3); a(n)=sum{k=0..floor(n/2), binomial(k, n-2k)+binomial(k-1, n-2k-1)}.

a(n)=-a(n-1)+a(n-2)+2a(n-3)+a(n-4).

Inverse binomial transform of A135364. - Paul Curtz, Apr 25 2008

MATHEMATICA

CoefficientList[Series[(1+2x)/((1+x)(1-x^2-x^3)), {x, 0, 50}], x] (* or *) LinearRecurrence[{-1, 1, 2, 1}, {1, 1, 0, 3}, 50] (* Harvey P. Dale, Dec 14 2011 *)

CROSSREFS

Cf. A000931, A077883.

Sequence in context: A077150 A065453 A152770 * A113486 A108572 A322335

Adjacent sequences:  A098598 A098599 A098600 * A098602 A098603 A098604

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 17 2004

STATUS

approved

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Last modified July 15 14:07 EDT 2019. Contains 325030 sequences. (Running on oeis4.)