A176338 a(n) = 1 + (1-3^n)*a(n-1) for n >=1, a(0) = 0.

0, 1, -7, 183, -14639, 3542639, -2579041191, 5637784043527, -36983863325537119, 727916397973221576159, -42982007467522787629036631, 7614090694841791737333323035127, -4046432358866721800888421193787892879

Offset: 0

Author

Roger L. Bagula, Apr 15 2010

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..64

Crossrefs

Cf. A176337.

Programs

GAP

a:= function(n,q)
    if n=0 then return 0;
    else return 1 - (q^n-1)*a(n-1,q);
fi; end; List([0..15], n-> a(n,3) ); # G. C. Greubel, Dec 07 2019

Magma

function a(n,q)
  if n eq 0 then return 0;
  else return 1 - (q^n-1)*a(n-1,q);
  end if; return a; end function;
[a(n,3): n in [0..15]]; // G. C. Greubel, Dec 07 2019

Maple

A176338 := proc(n)
    if n = 0 then
        0;
    else
        1+(1-3^n)*procname(n-1) ;
    end if;
end proc: # R. J. Mathar, May 04 2013

Mathematica

a[n_, q_]:= a[n, q]= If[n==0, 0, (1-q^n)*a[n-1, q] +1]; Table[a[n, 3], {n,0,15}]
nxt[{n_,a_}]:={n+1,a(1-3^(n+1))+1}; NestList[nxt,{0,0},20][[;;,2]] (* Harvey P. Dale, Dec 31 2024 *)

PARI

q=3; a(n,q) = if(n==0, 0, 1 -(q^n-1)*a(n-1,q) );
vector(16, n, a(n-1,3)) \\ G. C. Greubel, Dec 07 2019

Sage

def a(n, q):
    if (n==0): return 0
    else: return 1 - (q^n-1)*a(n-1,q)
[a(n,3) for n in (0..15)] # G. C. Greubel, Dec 07 2019