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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 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.)