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Search: id:A064017
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| A064017 |
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Number of ternary trees (A001764) with n nodes and maximal diameter. |
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+0
7
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| 1, 3, 12, 45, 162, 567, 1944, 6561, 21870, 72171, 236196, 767637, 2480058, 7971615, 25509168, 81310473, 258280326, 817887699, 2582803260, 8135830269, 25569752274, 80196041223, 251048476872, 784526490225, 2447722649502
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A problem important for polymer science because it counts the trees having unbranched branches; they are called "combs".
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,200
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FORMULA
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a(n) = 3*a(n-1)+3^(n-2); closed formula: (n+1)*3^(n-2).
a(n)=(n+2)3^(n-1)+0^n/3 (offset 0); a(n)=A025192(n)+A027471(n). - Paul Barry (pbarry(AT)wit.ie), Sep 05 2003
A006234(n+4) - a(n+2) = 3^n - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Mar 01 2005
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EXAMPLE
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a(5)=162 because we write (5+1)*3^(5-2)=6*3^3=6*27
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MAPLE
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a:=n->ceil(sum(3^(n-2), j=0..n)): seq(a(n), n=1..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2008
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP Code: lesforseq[ - 'i + 'j - 'kk' - 'ki' - 'kj' ], vesforseq(n) = 3^n, tesforseq = A006234
(PARI) { for (n=1, 200, if (n>1, a=(n + 1)*p; p*=3, a=p=1); write("b064017.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 06 2009]
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CROSSREFS
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Cf. A001764.
Cf. A014915, A027261, A079272.
Cf. A006234.
Sequence in context: A167477 A109437 A005656 this_sequence A005320 A062561 A128593
Adjacent sequences: A064014 A064015 A064016 this_sequence A064018 A064019 A064020
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Danail Bonchev (bonchevd(AT)aol.com), Sep 07 2001
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