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

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,4).

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)

Mathematica

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

Crossrefs

Cf. A140322.

Sequence in context: A048374 A226274 A184054 * A160653 A189436 A145950

Adjacent sequences: A140320 A140321 A140322 * A140324 A140325 A140326

Keyword

nonn,easy

Author

Paul Curtz, May 26 2008

Extensions

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

Status

approved