A084567 Binomial transform of (1,-1,4,-16,64,-256,1024,...) = (3*0^n-(-4)^n)/4.

1, 0, 3, -6, 21, -60, 183, -546, 1641, -4920, 14763, -44286, 132861, -398580, 1195743, -3587226, 10761681, -32285040, 96855123, -290565366, 871696101, -2615088300, 7845264903, -23535794706, 70607384121, -211822152360, 635466457083, -1906399371246

Offset: 0

Author

Paul Barry, May 30 2003

Keywords

• easy
• sign

Comments

Partial sums of (1,-1,3,-9,27,-81,....) (with g.f. (1+2x)/(1+3x) ).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,3)

Crossrefs

Cf. A054878 (absolute values).

Programs

Magma

I:=[1,0]; [n le 2 select I[n] else -2*Self(n-1)+3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 07 2013

Mathematica

CoefficientList[Series[(1 + 2 x)/((1 - x) (1 + 3 x)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 07 2013 *)
LinearRecurrence[{-2,3},{1,0},30] (* Harvey P. Dale, Aug 26 2024 *)

PARI

Vec((1+2*x)/((1-x)*(1+3*x))+O(x^66)) \\ Joerg Arndt, Jul 14 2013

Formula

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

G.f.: 1+ x -x/Q(0), where Q(k) = 1 + 3*x^2 + (3*k+4)*x - x*(3*k+1 + 3*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 07 2013

Extensions

Removed incorrect g.f. and e.g.f., Joerg Arndt, Jul 14 2013