A123950 Expansion of g.f.: x^2*(1-2*x) / (1-3*x-3*x^2+2*x^3).

0, 1, 1, 6, 19, 73, 264, 973, 3565, 13086, 48007, 176149, 646296, 2371321, 8700553, 31923030, 117128107, 429752305, 1576795176, 5785386229, 21227039605, 77883687150, 285761407807, 1048481205661, 3846960466104, 14114802199681, 51788325586033

Offset

1,4

References

Chang and Sederberg, Over and Over Again, MAA, 1997, Chapter 30

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

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

a(n) = A100191(n-2) for n > 2. - Georg Fischer, Oct 21 2018

Maple

seq(coeff(series(x^2*(1-2*x)/(1-3*x-3*x^2+2*x^3), x, n+1), x, n), n = 1 .. 30); # Muniru A Asiru, Oct 21 2018

Mathematica

M = {{0, 0, 1}, {0, 2, -2}, {1, -2, 1}}; v[1] = {0, 0, 1}; v[n_]:=v[n]=M.v[n-1]; Table[v[n][[1]], {n, 30}]
CoefficientList[Series[x^2*(1-2*x)/(1-3*x-3*x^2+2*x^3), {x, 0, 30}], x] (* G. C. Greubel, Aug 05 2019 *)

Prog

(PARI) concat(0, Vec(-x^2*(2*x-1)/(2*x^3-3*x^2-3*x+1)+O(x^130))) \\ Colin Barker, Feb 10 2015
(PARI) a(n)=([0, 1, 0; 0, 0, 1; -2, 3, 3]^(n-1)*[0; 1; 1])[1, 1] \\ Charles R Greathouse IV, Jun 24 2015
(GAP) a:=[0, 1, 1];; for n in [4..30] do a[n]:=3*a[n-1]+3*a[n-2]-2*a[n-3]; od; a; # Muniru A Asiru, Oct 21 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x^2*(1-2*x)/(1-3*x-3*x^2+2*x^3) )); // G. C. Greubel, Aug 05 2019
(Sage) a=(x^2*(1-2*x)/(1-3*x-3*x^2+2*x^3)).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Aug 05 2019

Crossrefs

Cf. A100191.

Sequence in context: A259804 A060579 A183326 * A100191 A191585 A359190

Adjacent sequences: A123947 A123948 A123949 * A123951 A123952 A123953

Keyword

nonn,easy,less

Author

Roger L. Bagula and Gary W. Adamson, Oct 26 2006

Extensions

Definition replaced with the generating function by the Assoc. Eds. of the OEIS, Mar 28 2010

Status

approved