%I A048248
%S A048248 1,2,4,7,14,23,45,72,137,217,402,635,1149,1816,3221,5101,8898,14127,
%T A048248 24305,38688,65809
%N A048248 Possible traces of n-step walks on 1-D lattice, ignoring translations.
%C A048248 Translations discounted, so the sequence of visits <0,1,2,1,0> has trace 
               (2,2), as do <0,-1,0,1,0>, <0,-1,-2,-1,0>, etc.
%e A048248 a(4)=7 since a walk of 4 steps can leave traces (1,1,1,1), (1,1,2), (2,
               1,1), (2,2), (1,3), (3,1) and (4). Note that (1,2,1) is impossible.
%t A048248 For[size = 1, size < 10, size++, traces = {}; For[i = 0, i < 2^ size, 
               i++, thePath = IntegerDigits[i, 2, size]*2 - 1; loc = size + 2; theTrace 
               = Table[0, {z, -size - 1, size + 1}]; For[j = 1, j <= size, j++, 
               loc += thePath[[j]]; If[thePath[[j]] == 1, theTrace[[loc - 1]]++, 
               theTrace[[loc]]++ ];]; theTrace = Select[theTrace, # > 0 &]; If[ 
               ! MemberQ[traces, theTrace], traces = Append[traces, theTrace]];]; 
               Print[Length[traces]]]; - Sam Handler (sam_5_5_5_0(AT)yahoo.com), 
               Aug 17 2006
%Y A048248 Sequence in context: A054160 A034426 A000075 this_sequence A056180 A000076 
               A054169
%Y A048248 Adjacent sequences: A048245 A048246 A048247 this_sequence A048249 A048250 
               A048251
%K A048248 nonn,more
%O A048248 1,2
%A A048248 Tony Bartoletti (azb(AT)home.com)
%E A048248 More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 17 2006