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

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,1,-4).

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

Mathematica

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

Prog

(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
(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

Crossrefs

Sequence in context: A219596 A182251 A191597 * A316105 A137966 A304187

Adjacent sequences: A088553 A088554 A088555 * A088557 A088558 A088559

Keyword

nonn,easy

Author

Cino Hilliard, Nov 17 2003

Status

approved