Search: id:A064017
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%I A064017
%S A064017 1,3,12,45,162,567,1944,6561,21870,72171,236196,767637,2480058,7971615,
%T A064017 25509168,81310473,258280326,817887699,2582803260,8135830269,
%U A064017 25569752274,80196041223,251048476872,784526490225,2447722649502
%N A064017 Number of ternary trees (A001764) with n nodes and maximal diameter.
%C A064017 A problem important for polymer science because it counts the trees having 
               unbranched branches; they are called "combs".
%H A064017 Harry J. Smith, <a href="b064017.txt">Table of n, a(n) for n=1,...,200</
               a>
%F A064017 a(n) = 3*a(n-1)+3^(n-2); closed formula: (n+1)*3^(n-2).
%F A064017 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
%F A064017 A006234(n+4) - a(n+2) = 3^n - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), 
               Mar 01 2005
%e A064017 a(5)=162 because we write (5+1)*3^(5-2)=6*3^3=6*27
%p A064017 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
%o A064017 Floretion Algebra Multiplication Program, FAMP Code: lesforseq[ - 'i 
               + 'j - 'kk' - 'ki' - 'kj' ], vesforseq(n) = 3^n, tesforseq = A006234
%o A064017 (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]
%Y A064017 Cf. A001764.
%Y A064017 Cf. A014915, A027261, A079272.
%Y A064017 Cf. A006234.
%Y A064017 Sequence in context: A167477 A109437 A005656 this_sequence A005320 A062561 
               A128593
%Y A064017 Adjacent sequences: A064014 A064015 A064016 this_sequence A064018 A064019 
               A064020
%K A064017 nonn,nice,easy
%O A064017 1,2
%A A064017 Danail Bonchev (bonchevd(AT)aol.com), Sep 07 2001

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