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A077882 Expansion of x/((1-x)*(1-x^2-2*x^3)). 0
0, 1, 1, 2, 4, 5, 9, 14, 20, 33, 49, 74, 116, 173, 265, 406, 612, 937, 1425, 2162, 3300, 5013, 7625, 11614, 17652, 26865, 40881, 62170, 94612, 143933, 218953, 333158, 506820, 771065, 1173137, 1784706, 2715268, 4130981, 6284681, 9561518, 14546644, 22130881, 33669681 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n+1) gives diagonal sums of Riordan array (1/(1-x),x(1+2x)) and partial sums of A052947. - Paul Barry, Jul 18 2005

LINKS

Table of n, a(n) for n=0..42.

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

FORMULA

a(n) = a(n-1)+a(n-2)+a(n-3)-2*a(n-4) - Roger L. Bagula, Mar 25 2005

a(n+1)=sum{k=0..n, sum{j=0..floor(k/2), C(j, k-2j)2^(k-2j)}}; - Paul Barry, Jul 18 2005

MATHEMATICA

{{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {-2, 1, 1, 1}}.{a[n - 4], a[n - 3], a[n - 2], a[n - 1]} a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 2; a[n_Integer?Positive] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] - 2a[n - 4]; aa = Table[a[n], {n, 0, 200}] - Roger L. Bagula, Mar 25 2005

CoefficientList[Series[x/((1-x)(1-x^2-2x^3)), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 1, 1, -2}, {0, 1, 1, 2}, 50] (* Harvey P. Dale, Aug 17 2017 *)

CROSSREFS

Sequence in context: A073153 A073154 A238656 * A351293 A234273 A120939

Adjacent sequences: A077879 A077880 A077881 * A077883 A077884 A077885

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 17 2002

EXTENSIONS

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified January 31 18:34 EST 2023. Contains 359980 sequences. (Running on oeis4.)