A091005 Expansion of x^2/((1-2*x)*(1+3*x)).

0, 0, 1, -1, 7, -13, 55, -133, 463, -1261, 4039, -11605, 35839, -105469, 320503, -953317, 2876335, -8596237, 25854247, -77431669, 232557151, -697147165, 2092490071, -6275373061, 18830313487, -56482551853, 169464432775, -508359743893, 1525146340543

Offset: 0

Author

Paul Barry, Dec 13 2003

Keywords

• easy
• sign

Comments

Inverse binomial transform of A091002.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,6).

Crossrefs

Cf. A015441.

Programs

GAP

Concatenation([0], List([1..30], n -> (3*2^n + 2*(-3)^n)/30)); # G. C. Greubel, Feb 01 2019

Magma

[0] cat [(3*2^n + 2*(-3)^n)/30: n in [1..30]]; // G. C. Greubel, Feb 01 2019

Mathematica

a[n_]:=(MatrixPower[{{1,4},{1,-2}},n].{{1},{1}})[[2,1]]; Table[a[n],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
Join[{0, 0}, LinearRecurrence[{-1, 6}, {1, -1}, 30]] (* G. C. Greubel, Feb 01 2019 *)
CoefficientList[Series[x^2/((1-2x)(1+3x)),{x,0,30}],x] (* Harvey P. Dale, Apr 30 2022 *)

PARI

vector(30, n, n--; (3*2^n + 2*(-3)^n - 5*0^n)/30) \\ G. C. Greubel, Feb 01 2019

Sage

[0] + [(3*2^n + 2*(-3)^n)/30 for n in (1..30)] # G. C. Greubel, Feb 01 2019

Formula

2^n = A091003(n) + 3*A091004(n) + 6*a(n).

a(n) = (3*2^n + 2*(-3)^n - 5*0^n)/30.

E.g.f.: (3*exp(2*x) + 2*exp(-3*x) - 5)/30. - G. C. Greubel, Feb 01 2019