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%I #15 Sep 01 2021 18:33:00
%S 6,28,52,100,196,388,772,1540,3076,6148,12292,24580,49156,98308,
%T 196612,393220,786436,1572868,3145732,6291460,12582916,25165828,
%U 50331652,100663300,201326596,402653188,805306372,1610612740,3221225476
%N a(n)=6*2^n+4 (Bode Number A003461(n+2)) except for a(1)=6.
%C Sequence similar to Bode Numbers relevant to A079946 and numeric partitions.
%C 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).
%C 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 ...
%H Vincenzo Librandi, <a href="/A091307/b091307.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F a(1) = 6, a(2) = 28, a(n) = 2*a(n-1) - 4 for n > 2.
%F G.f.: 2*x*(3+5*x-10*x^2)/((1-x)*(1-2*x)). [Colin Barker, Mar 12 2012]
%e a(3) = 52 because we can write 52 = 2*28 - 4
%t 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 *)
%Y Except for initial term, same as A003461(n+2). Cf. A053445, A079946, A090774.
%K nonn
%O 1,1
%A _Alford Arnold_, Feb 21 2004
%E Edited by _M. F. Hasler_, Apr 07 2009