# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a052471 Showing 1-1 of 1 %I A052471 #22 Aug 16 2020 08:37:16 %S A052471 0,0,0,0,0,0,1,3,11,34,99,279,773,2103,5661,15160,40373,107355,285059, %T A052471 757273,2013177,5361100,14303274,38250297,102538714,275597098, %U A052471 742674804,2006661720,5436008057,14763754746,40196603110,109703958381,300091975184,822705857129 %N A052471 Number of noncaterpillar trees on n nodes (A000055-A005418). %H A052471 Alois P. Heinz, Table of n, a(n) for n = 1..1000 %H A052471 Eric Weisstein's World of Mathematics, Caterpillar Graph %p A052471 with(numtheory): %p A052471 b:= proc(n) option remember; `if`(n<=1, n, %p A052471 (add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1)) %p A052471 end: %p A052471 a:= n-> b(n) -(add(b(k) *b(n-k), k=0..n)-`if`(irem(n, 2)=0, %p A052471 b(n/2), 0))/2 -ceil(2^(n-4) + 2^(iquo(n-2, 2)-1)): %p A052471 seq(a(n), n=1..40); # _Alois P. Heinz_, May 18 2013 %t A052471 b[n_] := b[n] = If[n <= 1, n, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n - j], {j, 1, n-1}])/(n-1)]; a[n_] := b[n] - (Sum[b[k]*b[n-k], {k, 0, n}] - If[ Mod[n, 2] == 0, b[n/2], 0])/2 - Ceiling[2^(n-4) + 2^(Quotient[n-2, 2] - 1)]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Feb 19 2016, after _Alois P. Heinz_ *) %Y A052471 Cf. A000055, A005418. %K A052471 nonn %O A052471 1,8 %A A052471 _Eric W. Weisstein_ %E A052471 a(14) and up from _Eric W. Weisstein_, Jul 17 2004. # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE