A158935 a(n)= -3a(n-1)-3a(n-2)-2a(n-3), n>3. a(0)=4, a(1)=4, a(2)=-5, a(3)=4.

4, 4, -5, 4, -5, 13, -32, 67, -131, 256, -509, 1021, -2048, 4099, -8195, 16384, -32765, 65533, -131072, 262147, -524291, 1048576, -2097149, 4194301, -8388608, 16777219, -33554435, 67108864, -134217725, 268435453, -536870912, 1073741827, -2147483651

Offset: 0

Author

Paul Curtz, Mar 31 2009

Keywords

• sign
• easy

Comments

The third column of the array of differences described in A153130. The first two columns are in A158916 and A158987. Taking differences like in A158926 keeps the recurrence.

Also the inverse binomial transform of A153130 if the first two items of A153130 are omitted.

Links

• Index entries for linear recurrences with constant coefficients, signature (-3, -3, -2).

Programs

Mathematica

Join[{4},LinearRecurrence[{-3,-3,-2},{4,-5,4},50]] (* Harvey P. Dale, May 25 2011 *)

Formula

a(n)= A154589(n) + A099838(n+2).

G.f.: (4+16*x+19*x^2+9*x^3)/((2*x+1)*(1+x+x^2)). - R. J. Mathar, Apr 08 2009

Extensions

Partially edited and extended by R. J. Mathar, Apr 08 2009

Edited by N. J. A. Sloane, Apr 08 2009