A109975 Second differences of A045623, prefixed by an initial 1.

1, 2, 4, 9, 20, 44, 96, 208, 448, 960, 2048, 4352, 9216, 19456, 40960, 86016, 180224, 376832, 786432, 1638400, 3407872, 7077888, 14680064, 30408704, 62914560, 130023424, 268435456, 553648128, 1140850688, 2348810240

Offset: 0

Author

Paul Curtz, Jun 07 2007

Keywords

• nonn
• easy

Comments

Binomial transform of [1,1,1,2,1,3,1,...]. [From Paul Barry, Mar 18 2009]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Crossrefs

Essentially a duplicate of A034007.

Programs

Magma

I:=[1, 2, 4, 9]; [n le 4 select I[n] else 4*Self(n-1)-4*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Jun 27 2012

Mathematica

CoefficientList[Series[(1-2x+x^3)/(1-2x)^2,{x,0,40}],x] (* Vincenzo Librandi, Jun 27 2012 *)

PARI

a(n)=(n+6)<<(n-3)+(n<2) \\ Charles R Greathouse IV, Jun 01 2011

Formula

G.f.: (1-2x+x^3)/(1-2x)^2. [From Paul Barry, Mar 18 2009]

a(n) = 2^(n-3)*(n+6) with n>1, a(0)=1, a(1)=2 (see the PARI code). - Bruno Berselli, Jun 27 2012

G.f.: Q(0)/(1-x), where Q(k)= 1 + (k+1)*x/(1 - x - x*(1-x)/(x + (k+1)*(1-x)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Apr 25 2013