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, 6442450948, 12884901892

Offset: 1

Author

Alford Arnold, Feb 21 2004

Keywords

• nonn
• easy

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 ...

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

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

Programs

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 *)

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

Extensions

Edited by M. F. Hasler, Apr 07 2009