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

0,1

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).

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

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

Prog

(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

Crossrefs

Same recurrence as A131562, A158916, A158926.

Sequence in context: A340976 A023573 A138757 * A367857 A121258 A087421

Adjacent sequences: A158924 A158925 A158926 * A158928 A158929 A158930

Keyword

sign

Author

Paul Curtz, Mar 31 2009

Extensions

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

Status

approved