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Expansion of x*(1 + 2*x - 3*x^2 + 4*x^3) / (1 - x - x^2 + x^3 - x^4).
1

%I #19 Jan 29 2023 17:51:50

%S 0,1,3,1,7,6,15,15,31,37,68,89,151,209,339,486,767,1123,1743,2585,

%T 3972,5937,9067,13617,20719,31206,47375,71479,108367,163677,247940,

%U 374729,567359,857825,1298395,1963590,2971519,4494539,6800863,10287473,15565316

%N Expansion of x*(1 + 2*x - 3*x^2 + 4*x^3) / (1 - x - x^2 + x^3 - x^4).

%D Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 48.

%H Seiichi Manyama, <a href="/A322753/b322753.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1).

%F a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) for n>4. - _Colin Barker_, Jan 06 2019

%t CoefficientList[Series[(x + 2*x^2 - 3*x^3 + 4*x^4)/(1 - x - x^2 + x^3 - x^4), {x, 0, 50}], x] (* _Amiram Eldar_, Jan 11 2019 *)

%t LinearRecurrence[{1,1,-1,1},{0,1,3,1,7},50] (* _Harvey P. Dale_, Jan 29 2023 *)

%o (PARI) concat(0, Vec(x*(1 + 2*x - 3*x^2 + 4*x^3) / (1 - x - x^2 + x^3 - x^4) + O(x^50))) \\ _Colin Barker_, Jan 06 2019

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 25 2018