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%I
%S 1,1,2,3,6,10,17,30,52,90,156,271,470,815,1414,2453,4255,7381,12804,
%T 22211,38529,66836,115940,201120,348881,605201,1049837,1821143,
%U 3159121,5480100,9506282,16490465,28605867,49622350,86079461,149321296
%N Number of sequences with terms 1, 2 or 3 summing to n with no three consecutive 1's.
%F a(n) = a(n - 2) + 2a(n - 3) + 2a(n - 4) + a(n - 5)
%e a(4) = 6 as 3 + 1, 1 + 3, 2 + 2, 1 + 1 + 2, 1 + 2 + 1 and 2 + 1 + 1 (but not 1 + 1 + 1 + 1).
%p a[0]=a[1]=1 a[2]=2 a[3]=3 a[4]=6 a[n_] := a[n - 2] + 2a[n - 3] + 2a[n - 4] + a[n - 5]
%K easy,nonn
%O 0,3
%A Joel Lewis (jblewis(AT)fas.harvard.edu), Oct 28 2006
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