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

Author

Paul Curtz, Apr 18 2008

Keywords

• sign
• easy

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

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

Programs

Magma

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

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

Extensions

More terms from Bruno Berselli, Mar 28 2012