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Search: id:A135429
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| A135429 |
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Number of transitive reflexive binary relations R on n labeled elements where |{y : xRy}| <= 3 for all x. |
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+0
3
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| 1, 1, 4, 29, 210, 2116, 25522, 362832, 6000276, 113593688, 2434603356, 58523364604, 1565365441708, 46273309903536, 1502773485741816, 53336787604185656, 2059209704215556448, 86117458019804680576
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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A. P. Heinz (1990). Analyse der Grenzen und Moeglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universitaet Freiburg, Freiburg i. Br., Germany.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..100
Alois P. Heinz, Illustration with formula for a(n)
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FORMULA
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a(n) = see program.
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MAPLE
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with (combinat, stirling2); A006882 := proc(n) option remember; if n <= 1 then 1 else n*A006882(n-2); fi; end; A025035:= proc(n) option remember; (3*n)! /n! /(6^n); end; z:= proc(n) option remember; add (binomial (n, k+k) *A006882(k+k-1) *k^(n-k-k), k=0..floor(n/2)); end; r:= proc(n) option remember; n! * add (add (add (add (stirling2(e, d) *a^(d+i) *(a*(a+1)/2)^(n-i-i-e-d-a) /a! /(n-i-i-e-d-a)! /i! /e! /(2^i), a=0..(n-i-i-e-d)), d=0..min(e, n-i-i-e)), e=0..(n-i-i)), i=0..floor(n/2)); end; a:= proc(n) option remember; n! *add (add (A025035(i) *z(j) *r(n-3*i-j) /(3*i)! /j! /(n-3*i-j)!, j=0..(n-3*i)), i=0..floor(n/3)); end; seq (a(n), n=0..30);
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CROSSREFS
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Cf. A135312, A025035, A006882, A008277, A000142.
Sequence in context: A143551 A100022 A001883 this_sequence A079756 A087809 A140526
Adjacent sequences: A135426 A135427 A135428 this_sequence A135430 A135431 A135432
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 12 2007
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