A137444 a(n) = 2*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=4.

1, 4, 6, 4, -4, -16, -24, -16, 16, 64, 96, 64, -64, -256, -384, -256, 256, 1024, 1536, 1024, -1024, -4096, -6144, -4096, 4096, 16384, 24576, 16384, -16384, -65536, -98304, -65536, 65536, 262144, 393216, 262144, -262144, -1048576, -1572864, -1048576, 1048576

Offset

0,2

Comments

Sequence opposite to its second differences.

Degenerate case of a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) with n > 3 (for which the sequence is identical to its fourth differences).

Links

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (2,-2).

Formula

G.f.: (1+2*x)/(1-2*x+2*x^2). - Colin Barker, Mar 28 2012

a(n) = (1/2 + 3*i/2)*(1 - i)^n + (1/2 - 3*i/2)*(1 + i)^n, n >= 0, where i=sqrt(-1). - Taras Goy, Apr 20 2019

Prog

(Magma) m:=41; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x)/(1-2*x+2*x^2))); // Bruno Berselli, Mar 28 2012

Crossrefs

Sequence in context: A214900 A362817 A078385 * A137429 A132024 A092039

Adjacent sequences: A137441 A137442 A137443 * A137445 A137446 A137447

Keyword

sign,easy

Author

Paul Curtz, Apr 18 2008

Extensions

More terms from Bruno Berselli, Mar 28 2012

Status

approved