A249992 Expansion of 1/((1+x)*(1+2*x)*(1-3*x)).

1, 0, 7, 6, 49, 84, 379, 882, 3157, 8448, 27391, 78078, 242425, 710892, 2165443, 6430794, 19423453, 58008216, 174548935, 522598230, 1569891841, 4705481220, 14124832267, 42357719586, 127106713189, 381253030704, 1143893309839, 3431411494062, 10294771353097

Offset: 0

Author

Alex Ratushnyak, Dec 27 2014

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,7,6).

Crossrefs

Cf. A249993.

Cf. A000392: expansion of x^3/((1-x)*(1-2*x)*(1-3*x)).

Cf. A091002: expansion of x^2/((1-x)*(1+2*x)*(1-3*x)).

Cf. A094705: expansion of x/((1+x)*(1-2*x)*(1-3*x)).

Programs

Magma

[(3^(n+2) + (-1)^n*(2^(n+4) - 5))/20: n in [0..50]]; // G. C. Greubel, Jul 21 2022

Maple

seq((9/20)*3^n+(4/5)*(-2)^n-(1/4)*(-1)^n, n=0 .. 100); # Robert Israel, Dec 28 2014

Mathematica

LinearRecurrence[{0, 7, 6}, {1, 0, 7}, 29] (* Jean-François Alcover, Oct 05 2017 *)
CoefficientList[Series[1/((1+x)(1+2x)(1-3x)),{x,0,30}],x] (* Harvey P. Dale, May 26 2020 *)

PARI

Vec(1/((1+x)*(1+2*x)*(1-3*x)) + O(x^50)) \\ Michel Marcus, Dec 28 2014

SageMath

[(3^(n+2) +(-1)^n*(2^(n+4) -5))/20 for n in (0..50)] # G. C. Greubel, Jul 21 2022

Formula

G.f.: 1/((1+x)*(1+2*x)*(1-3*x)).

a(n) = ( 3^(n+2) + (2^(n+4) - 5)*(-1)^n )/20. - Colin Barker, Dec 28 2014

a(n) = 7*a(n-2) + 6*a(n-3). - Colin Barker, Dec 28 2014

E.g.f.: (9/20)*exp(3*x) + (4/5)*exp(-2*x) - (1/4)*exp(-x). - Robert Israel, Dec 28 2014