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A033472
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Number of n-vertex labeled graphs that are gracefully labeled trees.
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0
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1, 1, 2, 4, 12, 40, 164, 752, 4020, 23576, 155632, 1112032, 8733628, 73547332, 670789524, 6502948232, 67540932632, 740949762580, 8634364751264, 105722215202120, 1366258578159064, 18468456090865364, 262118487952306820
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The gp/pari program below uses the Matrix-Tree Theorem and sums over {1,-1} vectors to isolate the multilinear term. It takes time 2^n * n^O(1) to compute graceful_tree_count(n). - Noam D. Elkies (elkies(AT)math.harvard.edu), Nov 18 2002
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LINKS
| Index entries for sequences related to trees
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EXAMPLE
| For n=3 we have 1-3-2 and 2-1-3, so a(3)=2.
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PROG
| (PARI) { treedet(v, n) = n=length(v); matdet(matrix(n, n, i, j, if(i-j, -v[abs(i-j)], sum(m=1, n+1, if(i-m, v[abs(i-m)], 0))))) } { graceful_tree_count(n, s, v, v1, v0)= if(n==1, 1, s=0; v1=vector(n-1, m, 1); v0=vector(n-1, m, if(m==1, 1, 0)); for(m=2^(n-2), 2^(n-1)-1, v= binary(m) - v0; s = s + (-1)^(v*v1~) * treedet(v1-2*v) ); s/2^(n-2) ) }
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CROSSREFS
| Cf. A006967.
Sequence in context: A074034 A188479 A062962 * A134983 A090959 A126942
Adjacent sequences: A033469 A033470 A033471 * A033473 A033474 A033475
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KEYWORD
| nonn
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AUTHOR
| Glenn G. Chappell (gchappell(AT)semovm.semo.edu)
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