%I #25 Nov 05 2025 15:22:25

%S 1,6,26,99,353,1213,4078,13529,44518,145750,475683,1549457,5040985,

%T 16387962,53251549,172987342,561848146,1824633763,5925198353,

%U 19240299477,62475465318,202861776657,658698488006,2138801439710,6944686435779,22549338805857,73217410408753,237735772753266,771923874337397

%N Expansion of (1-x)/((1-2*x)*(1-5*x+6*x^2-x^3)).

%H Vincenzo Librandi, <a href="/A234267/b234267.txt">Table of n, a(n) for n = 0..200</a>

%H T. Mansour and M. Shattuck, <a href="https://arxiv.org/abs/1207.3755">Some enumerative results related to ascent sequences</a>, arXiv preprint arXiv:1207.3755 [math.CO], 2012. Also Discrete Math., 315-316 (2013), 29-41. See Lemma A.2.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-16,13,-2).

%F G.f.: (1-x)/((1-2*x)*(1-5*x+6*x^2-x^3)).

%F a(n) = 7*a(n-1)-16*a(n-2)+13*a(n-3)-2*a(n-4) for n>3, a(0)=1, a(1)=6, a(2)=26, a(3)=99. - _Philippe Deléham_, Dec 25 2013

%t CoefficientList[Series[(1 - x)/((1 - 2 x) (1 - 5 x + 6 x^2 - x^3)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)

%o (Magma) I:=[1,6,26,99]; [n le 4 select I[n] else 7*Self(n-1)-16*Self(n-2)+13*Self(n-3)-2*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Apr 28 2014

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 23 2013