A140323 First differences of A140322.

1, 9, 31, 129, 511, 2049, 8191, 32769, 131071, 524289, 2097151, 8388609, 33554431, 134217729, 536870911, 2147483649, 8589934591, 34359738369, 137438953471, 549755813889, 2199023255551, 8796093022209, 35184372088831, 140737488355329, 562949953421311

Offset: 1

Author

Paul Curtz, May 26 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,4).

Crossrefs

Cf. A140322.

Programs

Mathematica

a[n_] := (2*4^n - (-1)^n); Array[a, 25, 0] (* Robert G. Wilson v, Aug 13 2011 *)

Formula

Mix A004171(2*n)-1, A004171(2*n+1)+1.

a(n+1)-4*a(n) = period 2: repeat [5, -5].

G.f.: x*(1 + 6*x)/(1 - 3*x - 4*x^2). - Ilya Gutkovskiy, May 11 2016

From Klaus Purath, Aug 03 2020: (Start)

a(n) = 8*A015521(n-1) + A102900(n-1).

a(n) = 30*4^(n-3) + a(n-2), n>2.

a(n+2) = 3*a(n+1) + 4*a(n). (End)

Extensions

Extended and offset changed from 0 to 1 by Vincenzo Librandi, Aug 09 2011