A158927 a(n) = -3a(n-1) - 3a(n-2) - 2a(n-3), n > 3.

2, 2, 2, -7, 11, -16, 29, -61, 128, -259, 515, -1024, 2045, -4093, 8192, -16387, 32771, -65536, 131069, -262141, 524288, -1048579, 2097155, -4194304, 8388605, -16777213, 33554432, -67108867, 134217731, -268435456, 536870909, -1073741821, 2147483648

Offset: 0

Author

Paul Curtz, Mar 31 2009

Keywords

• sign

Comments

The inverse binomial transform of A153130, after dropping A153130(0).

The inverse binomial transform of the full A153130 is A158916.

Dropping two initial terms of A153130 yields A158935, dropping three yields essentially a sign-reversed version of A158916, dropping 4 essentially the sequence here.

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..600
• Index entries for linear recurrences with constant coefficients, signature (-3, -3, -2).

Crossrefs

Same recurrence as A131562, A158916, A158926.

Programs

GAP

a := [2,2,2,-7];; for n in [5..10^3] do a[n] := -3*a[n-1] - 3*a[n-2] - 2*a[n-3]; od; a; # Muniru A Asiru, Jan 27 2018

Maple

a := proc(n) option remember: if n=0 then 2 elif n=1 then 2 elif n=2 then 2 elif n=3 then -7 elif n>=4 then -3*procname(n-1) - 3*procname(n-2) - 2*procname(n-3) fi; end:
seq(a(n), n=0..100); # Muniru A Asiru, Jan 27 2018

Formula

a(n) = -3a(n-1) - 3a(n-2) - 2a(n-3), with a(0)=a(1)=a(2)=2, a(3)=-7.

a(n) = (-1)^(n+1)*A157823(n) - A099838(n+3).

G.f.: (2+8*x+14*x^2+9*x^3)/((2*x+1)*(1+x+x^2)). - R. J. Mathar, Apr 09 2009

a(0)=2; a(n) = (1/2)*(-2)^n - 3*cos(2*Pi*n/3) + sqrt(3)*sin(2*Pi*n/3) for n >= 1. - Richard Choulet, Apr 23 2009

Extensions

Edited and extended by R. J. Mathar, Apr 09 2009