A138380 -id:A138380 - cp's OEIS frontend

A138382 First differences of A138380. Second differences of A138377.

1, -3, -1, -2, -4, 12, 4, 8, 16, -48, -16, -32, -64, 192, 64, 128, 256, -768, -256, -512, -1024, 3072, 1024, 2048, 4096, -12288, -4096, -8192, -16384, 49152, 16384, 32768, 65536, -196608, -65536, -131072, -262144, 786432, 262144, 524288, 1048576, -3145728

Offset: 0

Paul Curtz, May 08 2008

Index entries for linear recurrences with constant coefficients, signature (0,0,0,-4).

Cf. A138380, A138377.

Differences[LinearRecurrence[{0,0,0,-4},{0,1,3,2},60],2] (* Harvey P. Dale, Mar 19 2012 *)
LinearRecurrence[{0, 0, 0, -4},{1, -3, -1, -2},42] (* Ray Chandler, Aug 03 2015 *)

a(n) = -4*a(n-4).

Definition corrected by R. J. Mathar, May 09 2008

More terms from Harvey P. Dale, Mar 19 2012

A138377 a(0) = 0, a(1) = 1, a(2) = 3, a(3) = 2; thereafter a(n) = -4*a(n-4).

Original entry on oeis.org

0, 1, 3, 2, 0, -4, -12, -8, 0, 16, 48, 32, 0, -64, -192, -128, 0, 256, 768, 512, 0, -1024, -3072, -2048, 0, 4096, 12288, 8192, 0, -16384, -49152, -32768, 0, 65536, 196608, 131072, 0, -262144, -786432, -524288, 0, 1048576, 3145728, 2097152, 0, -4194304, -12582912, -8388608, 0, 16777216, 50331648

Offset: 0

Paul Curtz, May 08 2008

First and third differences have only 2^n's.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, -4).

Cf. A138380, A138382.

LinearRecurrence[{0,0,0,-4},{0,1,3,2},60] (* Harvey P. Dale, Mar 19 2012 *)

x='x+O('x^25); Vec(x*(1+x)*(2*x+1)/((1-2*x+2*x^2)*(1+2*x+2*x^2))) \\ G. C. Greubel, Feb 20 2017

From R. J. Mathar, May 09 2008: (Start)
O.g.f.: x*(1+x)*(2*x+1)/((1-2*x+2*x^2)*(1+2*x+2*x^2)).
a(n) = (5*A009545(n) - A108520(n))/4. (End)

cp's OEIS Frontend

A138382 First differences of A138380. Second differences of A138377.

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