A008353 a(n) = 2^n*(2^(n+1) - n - 1).

1, 4, 20, 96, 432, 1856, 7744, 31744, 128768, 519168, 2085888, 8364032, 33501184, 134103040, 536625152, 2146959360, 8588820480, 34357379072, 137433972736, 549745328128, 2199001235456, 8796046884864, 35184275619840, 140737287028736, 562949533990912, 2251798941270016, 9007197442801664

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1500 (terms 0..172 from Vincenzo Librandi)

Index entries for linear recurrences with constant coefficients, signature (8,-20,16).

Formula

a(n) = Sum_{k=0..n+1} C(2*n+2, 2*k)-2*k(n-k+1)*C(n+1, k)/n, n>0. - Paul Barry, Feb 24 2005

a(n) = 8*a(n-1)-20*a(n-2)+16*a(n-3). - Colin Barker, Feb 26 2015

G.f.: -(8*x^2-4*x+1) / ((2*x-1)^2*(4*x-1)). - Colin Barker, Feb 26 2015

Mathematica

A008353[n_] := 2^n*(2^(n+1) - n - 1); Array[A008353, 30, 0] (* Paolo Xausa, Mar 09 2026 *)

Prog

(Magma) [2^n*(2^(n+1) - n - 1): n in [0..50]]; // Vincenzo Librandi, Apr 25 2011
(PARI) Vec(-(8*x^2-4*x+1)/((2*x-1)^2*(4*x-1)) + O(x^100)) \\ Colin Barker, Feb 26 2015

Crossrefs

a(n) = A066345(2*n+1).

a(n) = 1 for n=0, 4 * A008464(n-2) else.

Sequence in context: A218837 A254943 A099025 * A250162 A296665 A057087

Adjacent sequences: A008350 A008351 A008352 * A008354 A008355 A008356

Keyword

nonn,easy

Author

N. J. A. Sloane and J. H. Conway

Status

approved