A133212 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3), n > 3; a(0) = 1, a(1) = 4, a(2) = 12, a(3) = 32.

1, 4, 12, 32, 72, 144, 272, 512, 992, 1984, 4032, 8192, 16512, 33024, 65792, 131072, 261632, 523264, 1047552, 2097152, 4196352, 8392704, 16781312, 33554432, 67100672, 134201344, 268419072, 536870912, 1073774592, 2147549184

Offset

0,2

Comments

Conjecture: a(n) = 2*A038503(n+3) if n > 0. - R. J. Mathar, Oct 23 2007

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4).

Formula

Sequence is identical to its fourth differences.

From R. J. Mathar, Nov 18 2007: (Start)

G.f.: -(1 + 2*x^2 + 4*x^3)/((2*x - 1)*(2*x^2 - 2*x + 1)). - [Corrected by Georg Fischer, May 12 2019]

a(n) = -2*(-1)^n*A009116(n)+3*2^n. (End)

E.g.f.: exp(x)*(3*cosh(x) - 2*(cos(x) + sin(x)) + 5*sinh(x)). - Stefano Spezia, Jan 03 2023

Maple

A133212 := proc(n) option remember ; if n <= 3 then op(n+1, [1, 4, 12, 32]) ; else 4*A133212(n-1)-6*A133212(n-2)+4*A133212(n-3) ; fi ; end: seq(A133212(n), n=0..50) ; # R. J. Mathar, Oct 23 2007

Mathematica

Join[{1}, LinearRecurrence[{4, -6, 4}, {4, 12, 32}, 29]] (* Ray Chandler, Sep 23 2015 *)

Crossrefs

Cf. A009116, A038503, A099087.

Sequence in context: A233458 A335687 A348864 * A233447 A127811 A361099

Adjacent sequences: A133209 A133210 A133211 * A133213 A133214 A133215

Keyword

nonn,easy

Author

Paul Curtz, Oct 11 2007

Extensions

More terms from R. J. Mathar, Oct 23 2007

Status

approved