A048497 a(n) = 2^(n-1)*(4*n - 6) + 4.

1, 2, 8, 28, 84, 228, 580, 1412, 3332, 7684, 17412, 38916, 86020, 188420, 409604, 884740, 1900548, 4063236, 8650756, 18350084, 38797316, 81788932, 171966468, 360710148, 754974724, 1577058308, 3288334340, 6845104132

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Equals binomial transform of A016813 preceded by a "1": (1, 1, 5, 9, 13, 21, ...). [Gary W. Adamson, Jan 13 2009]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Crossrefs

a(n) = T(3, n), array T given by A048494.

Cf. A016813. [Gary W. Adamson, Jan 13 2009]

Programs

Magma

[2^(n-1)*(4*n-6)+4: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011

Mathematica

LinearRecurrence[{5,-8,4},{1,2,8},30] (* Harvey P. Dale, Apr 16 2019 *)

Formula

From Colin Barker, Oct 07 2012: (Start)

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3).

G.f.: (1 - 3*x + 6*x^2)/((1-x)*(1-2*x)^2). (End)

Extensions

Formula from Ralf Stephan, Jan 15 2004