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 A078007 Expansion of (1-x)/(1-x-2*x^2-x^3). 4
 1, 0, 2, 3, 7, 15, 32, 69, 148, 318, 683, 1467, 3151, 6768, 14537, 31224, 67066, 144051, 309407, 664575, 1427440, 3065997, 6585452, 14144886, 30381787, 65257011, 140165471, 301061280, 646649233, 1388937264, 2983297010, 6407820771, 13763352055, 29562290607 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Let X = the 3x3 matrix [0,1,0; 0,0,1; 1,2,1]. a(n) = center term of X^n; but A002478(n) = term (3,3) of X^n. - Gary W. Adamson, May 30 2008 First bisection of A058278. - Oboifeng Dira, Aug 04 2016 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,2,1). FORMULA a(n) = a(n-1) + 2*a(n-2) + a(n-3). - Ilya Gutkovskiy, Aug 06 2016 MATHEMATICA LinearRecurrence[{1, 2, 1}, {1, 0, 2}, 40] (* or *) CoefficientList[Series[(1 -x)/(1-x-2*x^2-x^3), {x, 0, 40}], x] (* G. C. Greubel, Jun 28 2019 *) PROG (PARI) Vec((1-x)/(1-x-2*x^2-x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 26 2012 (MAGMA) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-x-2*x^2-x^3) )); // G. C. Greubel, Jun 28 2019 (Sage) ((1-x)/(1-x-2*x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 28 2019 (GAP) a:=[1, 0, 2];; for n in [4..40] do a[n]:=a[n-1]+2*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Jun 28 2019 CROSSREFS First differences of A002478. Cf. A058278. Sequence in context: A076993 A076698 A323598 * A198683 A001932 A213920 Adjacent sequences:  A078004 A078005 A078006 * A078008 A078009 A078010 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 17 2002 STATUS approved

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Last modified October 14 15:03 EDT 2019. Contains 328019 sequences. (Running on oeis4.)