A088556 Numbers of the form (4^n + 4^(n-1) + ... + 1) + (n mod 2).

6, 21, 86, 341, 1366, 5461, 21846, 87381, 349526, 1398101, 5592406, 22369621, 89478486, 357913941, 1431655766, 5726623061, 22906492246, 91625968981, 366503875926, 1466015503701, 5864062014806, 23456248059221, 93824992236886, 375299968947541, 1501199875790166

Offset: 1

Author

Cino Hilliard, Nov 17 2003

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,1,-4).

Crossrefs

Cf. A002450, A047849.

Programs

Magma

I:=[6,21,86]; [n le 3 select I[n] else 4*Self(n-1)+Self(n-2)-4*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 14 2015

Mathematica

LinearRecurrence[{4, 1, -4}, {6, 21, 86}, 50] (* Vincenzo Librandi, Jun 14 2015 *)

PARI

trajpolypn(n1) = { for(x1=1,n1, y1 = polypn(4,x1); print1(y1",") ) }
polypn(n,p) = { x=n; if(p%2,y=2,y=1); for(m=1,p, y=y+x^m; ); return(y) }

PARI

Vec(x*(6-3*x-4*x^2)/((1-x)*(1+x)*(1-4*x)) + O(x^30)) \\ Colin Barker, Jun 13 2015

Formula

If n is even, then 4^n + ... + 1 = (4^(n+1) - 1)/3 = (2^(n+1) - 1)*(2^(n+1) + 1)/3. - R. K. Guy, Nov 17 2003

a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3). - Colin Barker, Apr 02 2012

G.f.: x*(6-3*x-4*x^2) / ((1-x)*(1+x)*(1-4*x)). - Colin Barker, Apr 02 2012