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 A338987 Number of rooted graceful labelings with n edges. 2
 1, 1, 2, 6, 24, 108, 596, 3674, 26068, 202470, 1753884, 16435754, 168174596, 1842418704, 21757407158, 272771715272, 3649515044178, 51532670206504, 770442883634326, 12093451621846094, 199856952123506304, 3452120352032161404, 62471981051497913826, 1177664861561125869100, 23163177237781937250558 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A graceful labeling of a graph with n edges assigns distinct labels l(v) to the vertices such that  0<=l(v)<=n and the n differences |l(u)-l(v)| between labels of adjacent vertices are distinct. It is rooted if, in addition, either |l(u)-l(w)|>|l(u)-l(v)| for some neighbor of u or |l(v)-l(w)|>|l(u)-l(v)| for some neighbor of v, whenever |l(u)-l(v)|0. LINKS David A. Sheppard, The factorial representation of major balanced labelled graphs, Discrete Math., Vol. 15, No. 4 (1976), 379-388. EXAMPLE a(5) = 108 < 120 = 5!, because 0--5,0--4,0--3,3--5,1--2 and 0--5,1--5,2--5,0--2,1--3 are forbidden, as well as five each beginning with 0--5,0--4,2--5,1--3 and 0--5,1--4,0--3,2--4. PROG (Python) def solve(d, m_in): ....global _n, _cache ....args = (d, m_in) ....if args in _cache: ........return _cache[args] ....if d == 0: ........rv = 1 ....else: ........rv = 0 ........m_test = 1 | (1<

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Last modified January 27 10:39 EST 2022. Contains 350607 sequences. (Running on oeis4.)