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
KEYWORD
nonn
AUTHOR
Alford Arnold, Feb 21 2004
EXTENSIONS
Edited by M. F. Hasler, Apr 07 2009
STATUS
approved