A091003 Expansion of (1-3*x^2)/((1-2*x)*(1+3*x)).

1, -1, 4, -10, 34, -94, 298, -862, 2650, -7822, 23722, -70654, 212986, -636910, 1914826, -5736286, 17225242, -51642958, 154994410, -464852158, 1394818618, -4183931566, 12552843274, -37656432670, 112973492314, -338912088334, 1016753042218

Offset: 0

Author

Paul Barry, Dec 13 2003

Keywords

• easy
• sign

Comments

Inverse binomial transform of A091000.

Links

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

Programs

GAP

Concatenation([1], List([1..30], n -> (2^n + 4*(-3)^n)/10)); # G. C. Greubel, Feb 01 2019

Magma

[1] cat [(2^n + 4*(-3)^n)/10: n in [1..30]]; // G. C. Greubel, Feb 01 2019

Mathematica

CoefficientList[Series[(1-3x^2)/((1-2x)(1+3x)),{x,0,30}],x] (* Harvey P. Dale, Dec 23 2014 *)
Join[{1}, LinearRecurrence[{-1,6}, {-1,4}, 30]] (* G. C. Greubel, Feb 01 2019 *)

PARI

vector(30, n, n--; (2^n + 4*(-3)^n + 5*0^n)/10) \\ G. C. Greubel, Feb 01 2019

Sage

[1] + [(2^n + 4*(-3)^n)/10 for n in (1..30)] # G. C. Greubel, Feb 01 2019

Formula

2^n = A091003(n) + 3*A091004(n) + 6*A091005(n).

a(n) = (2^n + 4*(-3)^n + 5*0^n)/10.

E.g.f.: (exp(2*x) + 4*exp(-3*x) + 5)/10. - G. C. Greubel, Feb 01 2019