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A000147
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Number of trees of diameter 5.
(Formerly M1741 N0690)
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0
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0, 0, 0, 0, 0, 1, 2, 7, 14, 32, 58, 110, 187, 322, 519, 839, 1302, 2015, 3032, 4542, 6668, 9738, 14006, 20036, 28324, 39830, 55473, 76875, 105692, 144629, 196585, 266038, 357952, 479664, 639519, 849425, 1123191, 1479972, 1942284, 2540674, 3311415
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| A tree of diameter 5 is formed from two rooted trees of height 2, with their roots joined. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006
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REFERENCES
| J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for sequences related to trees
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FORMULA
| If n odd, a(n)=sum_{k=1}^{(n-1)/2} b(k)*b(n-k); if n even, a(n)=(sum_{k=1}^{n/2-1} b(k)*b(n-k)) + C(b(n/2)+1, 2), where b(n)=P(n-1)-1=A000065(n-1). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006
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CROSSREFS
| Sequence in context: A034791 A140253 A018453 * A128902 A060552 A191396
Adjacent sequences: A000144 A000145 A000146 * A000148 A000149 A000150
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006
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