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Search: id:A007501
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| A007501 |
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a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.
(Formerly M0818)
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+0
20
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| 2, 3, 6, 21, 231, 26796, 359026206, 64449908476890321, 2076895351339769460477611370186681, 2156747150208372213435450937462082366919951682912789656986079991221
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Number of nonisomorphic complete binary trees with leaves colored using two colors - Brendan McKay (bdm(AT)cs.anu.edu.au), Feb 01, 2001
Let {t(k)} be the triangular numbers (A000219). Then a(0) = 2; for n>0, a(n) = t(a(n-1)). - Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 13 2004
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REFERENCES
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W. H. Cutler, Subdividing a Box into Completely Incongruent Boxes, J. Rec. Math., 12 (1979), 104-111.
J. V. Post, "Iterated Triangular Numbers", preprint.
J. V. Post, "Iterated Polygonal Numbers", preprint.
J. V. Post, "Triangular Carmichael Numbers: The First 22 Identified", preprint.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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G. L. Honaker, Jr., 41041 (another Prime Pages' Curiosity)
J. V. Post, Math Pages
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EXAMPLE
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Example for depth 2 (the nonisomorpic possibilites are AAAA, AAAB, AABB, ABAB, ABBB, BBBB):
.........o
......../.\
......./...\
......o.....o
...../.\.../.\
..../...\./...\
....A...B.B...B
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MATHEMATICA
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f[n_Integer] := n(n + 1)/2; NestList[f, 2, 10]
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PROGRAM
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(PARI) a(n)=if(n<1, 2, a(n-1)*(1+a(n-1))/2)
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CROSSREFS
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Equals A006893(n+1) + 1. Cf. A000217.
Cf. A129440.
Sequence in context: A012924 A024485 A013155 this_sequence A015773 A015768 A094470
Adjacent sequences: A007498 A007499 A007500 this_sequence A007502 A007503 A007504
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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