A091307 a(n)=6*2^n+4 (Bode Number A003461(n+2)) except for a(1)=6.

6, 28, 52, 100, 196, 388, 772, 1540, 3076, 6148, 12292, 24580, 49156, 98308, 196612, 393220, 786436, 1572868, 3145732, 6291460, 12582916, 25165828, 50331652, 100663300, 201326596, 402653188, 805306372, 1610612740, 3221225476

Offset

1,1

Comments

Sequence similar to Bode Numbers relevant to A079946 and numeric partitions.

A053445 describes certain partitions which start triangular arrays of all other numeric partitions; e.g. - 22, 33, 222, 44, 332, 2222, ... A079946 provides the indices for these partitions. (cf. A090324 and A090774).

By expanding the terms of a(n) in a similar manner, the vertex partitions can be readily indexed by noting that the indices increase by eight as follows: 6 28 (one case), 52 60 (two cases), 100 108 116 124 (four cases), 196 204 212 220 228 236 244 252 (eight cases), 388 ...

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(1) = 6, a(2) = 28, a(n) = 2*a(n-1) - 4 for n > 2.

G.f.: 2*x*(3+5*x-10*x^2)/((1-x)*(1-2*x)). [Colin Barker, Mar 12 2012]

Example

a(3) = 52 because we can write 52 = 2*28 - 4

Mathematica

CoefficientList[Series[2x (3+5x-10x^2)/((1-x)(1-2x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, -2}, {0, 6, 28, 52}, 40] (* Harvey P. Dale, Sep 01 2021 *)

Crossrefs

Except for initial term, same as A003461(n+2). Cf. A053445, A079946, A090774.

Sequence in context: A323752 A120624 A138873 * A254879 A298168 A317478

Adjacent sequences: A091304 A091305 A091306 * A091308 A091309 A091310

Keyword

nonn

Author

Alford Arnold, Feb 21 2004

Extensions

Edited by M. F. Hasler, Apr 07 2009

Status

approved