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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
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
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: A073154 A362609 A238656 * A351293 A363225 A234273
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