OFFSET

1,2

COMMENTS

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.

Trace as used here refers to the number of times an edge is used in the walk. - Sean A. Irvine, Jun 06 2021

LINKS

Sean A. Irvine, Java program (github)

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

a(19)-a(21) from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 17 2006

a(22)-a(30) from Sean A. Irvine, Jun 06 2021

STATUS

approved