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%I #17 Oct 15 2012 23:17:44
%S 0,1,1,2,4,8,16,32,63,126,252,502,1004,2008,4012,8024,16048,32089,
%T 64178,128356,256696,513392,1026784,2053538,4107076,8214152,16428241,
%U 32856482,65712964,131425806,262851612,525703224,1051406197,2102812394,4205624788,8411249081
%N Number of sequences of n 2's and 3's with curling number 2 and which have the form XY^2 with Y = 2.
%C Equals A217929 + A217930.
%H N. J. A. Sloane, <a href="/A217832/b217832.txt">Table of n, a(n) for n = 1..101</a>
%H <a href="/index/Cu#curling_numbers">Index entries for sequences related to curling numbers</a>
%F If n is a multiple of 3 then a(n) = 2a(n-1)-A217929(n/3), otherwise a(n) = 2a(n-1).
%F Comment from Paul Curtz, Oct 15 2012:
%F From a(n+3)=1, the terms taken in threes are: 1,2,4, 8,16,32, 63,126,252, ... (*).
%F a(n+4) - 2*a(n+3) = 0,0,0, 0,0,-1, 0,0,-2, 0,0,-4, 0,0,-7, 0,0,-16, 0,0,-30, 0,0,-63, 0,0,-122,... . See -A217929. This is the formula given above.
%F 2^n - (*) = 0,0,0,0,0,0,1,2,4,10,20,40,84,168,336,679,1358,2716,5448,...
%F = b(n) with offset 0. Hence a second formula:
%F b(n+1)-2*b(n)=0,0,0,0,0,1,0,0,2,0,0,4,0,0,7,0,0,16,... . (End)
%Y Cf. A217929, A217930, A217931.
%K nonn
%O 1,4
%A _N. J. A. Sloane_, Oct 15 2012
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