A134142 List of quadruples: 2*(-4)^n, -3*(-4)^n, 2*(-4^n), 2*(-4)^n, n >= 0.

2, -3, 2, 2, -8, 12, -8, -8, 32, -48, 32, 32, -128, 192, -128, -128, 512, -768, 512, 512, -2048, 3072, -2048, -2048, 8192, -12288, 8192, 8192, -32768, 49152, -32768, -32768, 131072, -196608, 131072, 131072, -524288, 786432, -524288, -524288, 2097152, -3145728, 2097152, 2097152, -8388608

Offset: 0

Author

Paul Curtz, Jan 29 2008

Keywords

• tabf
• easy
• sign

Links

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

Crossrefs

Cf. A081147, A038521.

Programs

Maple

A134142 := proc(n) (-4)^floor(n/4)*op(1+(n mod 4), [2,-3,2,2]) ; end: for n from 0 to 80 do printf("%d ",A134142(n)) ; od: # R. J. Mathar, Feb 05 2008

Formula

O.g.f.: (x+2)/(2*x^2+2*x+1). a(n) = 2*A108520(n)+A108520(n-1). - R. J. Mathar, Feb 05 2008

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

a(n) = -2*a(n-1)-2*a(n-2) for n > 1. - Chai Wah Wu, May 19 2025

E.g.f.: exp(-x)*(2*cos(x) - sin(x)). - Stefano Spezia, May 19 2025

Extensions

More terms from R. J. Mathar, Feb 05 2008