A122299 Expansion of x * (1-x) / ( 1 - 2*x - 3*x^2 + x^3 ).

0, 1, 1, 5, 12, 38, 107, 316, 915, 2671, 7771, 22640, 65922, 191993, 559112, 1628281, 4741905, 13809541, 40216516, 117119750, 341079507, 993301748, 2892722267, 8424270271, 24533405595, 71446899736, 208069745986, 605946785585, 1764655909392, 5139082429553

Offset

1,4

Comments

Essentially the same as A095310. - Georg Fischer, Oct 07 2018

Links

Muniru A Asiru, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (2,3,-1)

Formula

a(n)= +2*a(n-1) +3*a(n-2) -a(n-3).

Maple

seq(coeff(series(x*(1-x)/(1-2*x-3*x^2+x^3), x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 07 2018

Mathematica

CoefficientList[Series[x*(1-x)/(1-2*x-3*x^2+x^3), {x, 0, 30}], x] (* G. C. Greubel, Oct 08 2018 *)

Prog

(GAP) a:=[0, 1, 1];; for n in [4..30] do a[n]:=2*a[n-1]+3*a[n-2]-a[n-3]; od; a; # Muniru A Asiru, Oct 07 2018
(Magma) I:=[0, 1, 1]; [n le 3 select I[n] else 2*Self(n-1)+3*Self(n-2)-Self(n-3): n in [1..30]]; // Vincenzo Librandi, Oct 08 2018
(PARI) x='x+O('x^30); concat([0], Vec(x*(1-x)/(1-2*x-3*x^2+x^3))) \\ G. C. Greubel, Oct 08 2018

Crossrefs

Sequence in context: A220705 A034752 A095310 * A162269 A028322 A169588

Adjacent sequences: A122296 A122297 A122298 * A122300 A122301 A122302

Keyword

nonn

Author

Gary W. Adamson and Roger L. Bagula, Oct 19 2006

Status

approved